WEBVTT mathematics/basic-math/pyo
00:00:00.400 --> 00:00:01.900
Welcome back to Educator.com.
00:00:01.900 --> 00:00:06.900
For the next lesson, we are going to go over probability of compound events
00:00:06.900 --> 00:00:12.600
and those events being independent and dependent.
00:00:12.600 --> 00:00:17.500
Before we go over these events, let's first review over probability.
00:00:17.500 --> 00:00:23.700
Probability is talking about the chances of something happening.
00:00:23.700 --> 00:00:29.800
What is the probability of picking a card from a deck?
00:00:29.800 --> 00:00:34.900
Or what is the probability of rolling a 2 if you roll a die?
00:00:34.900 --> 00:00:40.400
Probability talks about your chances of something occurring.
00:00:40.400 --> 00:00:55.500
To find probability, we are looking at a ratio; a ratio is like a fraction.
00:00:55.500 --> 00:00:58.300
It is comparing the top number with the bottom number.
00:00:58.300 --> 00:01:12.300
Probability is talking about your desired outcome or the outcome that you are looking for
00:01:12.300 --> 00:01:21.100
over the total possible number of outcomes or just total for short.
00:01:21.100 --> 00:01:25.500
It is desired outcome over the total--is the probability.
00:01:25.500 --> 00:01:29.600
Probability, once you have this, you can leave it as a fraction.
00:01:29.600 --> 00:01:33.900
You can change it to a decimal; it is just fraction to decimal.
00:01:33.900 --> 00:01:37.700
You just divide the top number with the bottom number.
00:01:37.700 --> 00:01:40.800
Or you can change it to a percent.
00:01:40.800 --> 00:01:51.800
Usually probability is left as a fraction, desired outcome over the total.
00:01:51.800 --> 00:02:02.500
If I have a die, a number cube... we are going to talk about number cubes in our examples later.
00:02:02.500 --> 00:02:10.900
A number cube has different numbers of dots on each side.
00:02:10.900 --> 00:02:15.500
There is 6 sides; each side has a different number, 1 through 6.
00:02:15.500 --> 00:02:22.300
If I said what is the probability, what are the chances of rolling a 1?
00:02:22.300 --> 00:02:27.800
My desired outcome then, I am going to say my probability of rolling a 1.
00:02:27.800 --> 00:02:34.200
That is how we write it out, probability of rolling a 1.
00:02:34.200 --> 00:02:42.200
That is my desired outcome; how many sides has a 1?--only 1 side.
00:02:42.200 --> 00:02:50.000
My desired outcome, there is only 1; over... how many total sides are there?
00:02:50.000 --> 00:02:53.400
How many total possible outcomes are there?
00:02:53.400 --> 00:02:56.100
There is 6 sides; my total is 6.
00:02:56.100 --> 00:03:01.100
The probability of rolling a 1 is 1/6.
00:03:01.100 --> 00:03:05.700
Same thing if I said probability of rolling a 3.
00:03:05.700 --> 00:03:10.000
Be careful, this number is not going to be the number on top.
00:03:10.000 --> 00:03:15.800
How many sides have a 3?--only 1 side.
00:03:15.800 --> 00:03:25.000
My desired outcome would be just 1 because there is only 1 possible side that is going to be a 3.
00:03:25.000 --> 00:03:29.900
It is 1 over... how many total sides are there?--6.
00:03:29.900 --> 00:03:34.200
The chances of rolling a 1 is the same as the chance of rolling a 3.
00:03:34.200 --> 00:03:38.200
That is probability.
00:03:38.200 --> 00:03:43.800
When we talk about two events, each of this, this is one event.
00:03:43.800 --> 00:03:48.100
You are rolling a 1; this is another event, rolling a 3.
00:03:48.100 --> 00:03:50.800
Each of those are events.
00:03:50.800 --> 00:03:55.700
We are talking about when we have two events or two or more events.
00:03:55.700 --> 00:03:59.700
When we have two events, when there is two things going on,
00:03:59.700 --> 00:04:05.800
those two events can be either independent events or dependent events.
00:04:05.800 --> 00:04:08.100
That is what we are talking about now.
00:04:08.100 --> 00:04:16.600
Independent events is when the outcome of the second event does not depend on the outcome of the first event.
00:04:16.600 --> 00:04:19.200
Think about what the word independent means.
00:04:19.200 --> 00:04:26.000
It doesn't depend on it; it is not affected by anyone else, anything else.
00:04:26.000 --> 00:04:32.900
The first event happens; the second event happens; they don't affect each other.
00:04:32.900 --> 00:04:40.300
When you have two events that are independent, then we write each of those events as A and B.
00:04:40.300 --> 00:04:45.100
It is probability of A, that is the first event.
00:04:45.100 --> 00:04:49.200
The probability of B, that is the second event.
00:04:49.200 --> 00:04:54.200
When we have two events that are independent, all we have to do is multiply
00:04:54.200 --> 00:05:01.100
the probability of that first event with the probability of the second event.
00:05:01.100 --> 00:05:09.500
Let's say I have a bag of marbles.
00:05:09.500 --> 00:05:16.600
In this bag, I have 1, 2, 3 red marbles.
00:05:16.600 --> 00:05:22.800
Let's say I have 2, 3, 4 blue marbles.
00:05:22.800 --> 00:05:28.500
And let's say I have 2 green; I don't have green.
00:05:28.500 --> 00:05:32.800
So I am going to just use black for green; I will put G for green.
00:05:32.800 --> 00:05:38.900
3 red marbles, 4 blue, and 2 green marbles; I have a bag of marbles.
00:05:38.900 --> 00:05:45.700
Just talking about one event, let's just say what is the probability of picking a red marble?
00:05:45.700 --> 00:05:49.800
That is one event because I am going to pick up one marble.
00:05:49.800 --> 00:05:58.200
The probability of picking a red, that red is my desired outcome.
00:05:58.200 --> 00:06:01.300
That is what I am asking for.
00:06:01.300 --> 00:06:05.800
How many reds do I have?--I have 3 reds.
00:06:05.800 --> 00:06:09.200
That number, the desired outcome, is going to go on top.
00:06:09.200 --> 00:06:15.200
3 over... how many total number of marbles do I have?
00:06:15.200 --> 00:06:21.500
I have 1, 2, 3, 4, 5, 6, 7, 8, 9.
00:06:21.500 --> 00:06:24.100
If you have a fraction, you always have to simplify.
00:06:24.100 --> 00:06:30.100
I can simplify this by 3; divide each by 3.
00:06:30.100 --> 00:06:39.600
It is going to become 1/3; the probability of picking a red marble is 1/3.
00:06:39.600 --> 00:06:42.400
That is only when you have one event.
00:06:42.400 --> 00:06:47.700
Talking about compound events, two events, if I ask for
00:06:47.700 --> 00:06:59.700
the probability of picking a red and afterwards picking a blue...
00:06:59.700 --> 00:07:05.400
Probability of picking a red, we already found that; that is 1/3.
00:07:05.400 --> 00:07:19.900
It is going to be probability of picking red times the probability of picking the blue.
00:07:19.900 --> 00:07:27.100
The only way both of these events, picking the red and then picking another marble the blue,
00:07:27.100 --> 00:07:34.800
the only way these two events are going to be independent is if after we pick the red marble,
00:07:34.800 --> 00:07:40.700
after this first event, after you pick the first marble, you have to place it back into the bag.
00:07:40.700 --> 00:07:43.800
You are going to pick one out; put it back in.
00:07:43.800 --> 00:07:46.600
Then pick the second one.
00:07:46.600 --> 00:07:54.300
It will be independent because then picking this red or picking this one, it won't affect this one.
00:07:54.300 --> 00:08:03.800
Probability of picking a red marble, we know that is 3/9 or 1/3.
00:08:03.800 --> 00:08:09.300
Times probability of picking a blue.
00:08:09.300 --> 00:08:14.200
Blue is my desired outcome; I have 4.
00:08:14.200 --> 00:08:23.200
Over a total number of 4, 5, 6, 7, 8, 9.
00:08:23.200 --> 00:08:30.100
Again after you pick the first marble, we put it back in the bag.
00:08:30.100 --> 00:08:34.700
Now it is just original number of marbles,
00:08:34.700 --> 00:08:39.100
the same number of marbles when we picked the blue one, when we picked the second one.
00:08:39.100 --> 00:08:47.500
This is 1 times 4 is 4; over... 3 times 9 is 27.
00:08:47.500 --> 00:08:53.500
This can't be simplified; this is our answer.
00:08:53.500 --> 00:09:04.800
The probability of picking a red and then after replacing it, picking a blue, would be 4/27.
00:09:04.800 --> 00:09:12.900
This is independent events.
00:09:12.900 --> 00:09:20.300
When we have two events and the second outcome is affected
00:09:20.300 --> 00:09:26.900
by the first outcome, then we have dependent events.
00:09:26.900 --> 00:09:33.100
The second event depends on the first event.
00:09:33.100 --> 00:09:41.500
Finding the probability of two dependent events is a little bit different.
00:09:41.500 --> 00:09:46.200
Same thing here; when we have probability of the first event A
00:09:46.200 --> 00:09:53.700
and then the probability of the second event B, we are still going to multiply them.
00:09:53.700 --> 00:10:04.800
It will be the probability of A times the probability of B after A because remember this second event is affected.
00:10:04.800 --> 00:10:11.700
It depends on the first event A.
00:10:11.700 --> 00:10:31.300
Back to the bag of marbles; again 3 red, 4 blue, and 2 green marbles.
00:10:31.300 --> 00:10:37.600
Same bag of marbles; but now the way it becomes dependent events.
00:10:37.600 --> 00:10:48.100
I want to find the probability of picking a red and then my second event will be picking a blue.
00:10:48.100 --> 00:10:58.400
But the difference is here after we pick the first marble, after we find the probability of picking a red,
00:10:58.400 --> 00:11:01.300
we are not going to put the marble back in the bag.
00:11:01.300 --> 00:11:05.900
We are going to take it out; we are going to leave it out.
00:11:05.900 --> 00:11:09.700
Then the second event, the probability of picking a blue, is going to be
00:11:09.700 --> 00:11:15.300
slightly different because the total number of marbles is different.
00:11:15.300 --> 00:11:20.900
There is less marbles; that is why these would be dependent events.
00:11:20.900 --> 00:11:24.800
Because the probability of picking a blue is not going to be
00:11:24.800 --> 00:11:31.800
the same as if we were to place the marble back in.
00:11:31.800 --> 00:11:39.100
This will be probability of red times probability of blue.
00:11:39.100 --> 00:11:42.700
Again we are not going to replace it back in.
00:11:42.700 --> 00:11:48.900
The probability of picking a red, how many reds do I have?
00:11:48.900 --> 00:11:54.800
My desired outcome is 3; desired outcome goes on top.
00:11:54.800 --> 00:12:08.700
3 over... total number of marbles is 9; you can simplify this to become 1/3.
00:12:08.700 --> 00:12:17.800
Let's say that... let me just change this to 1/3.
00:12:17.800 --> 00:12:23.100
Because this red is no longer there, we took it out.
00:12:23.100 --> 00:12:25.300
That is the first event.
00:12:25.300 --> 00:12:34.800
For the second event, since this marble was not replaced back in, it is left out.
00:12:34.800 --> 00:12:36.300
This is going to be different.
00:12:36.300 --> 00:12:40.500
Probability of picking a blue, my desired outcome is number of blue.
00:12:40.500 --> 00:12:45.300
How many blues do I have?--4.
00:12:45.300 --> 00:12:48.300
My total number of marbles is going to be different.
00:12:48.300 --> 00:12:52.400
It is going to be 1, 2, 3, 4, 5, 6, 7, 8.
00:12:52.400 --> 00:12:55.300
It is going to be 1 less than the total here.
00:12:55.300 --> 00:12:59.500
This was originally 9 before we simplified.
00:12:59.500 --> 00:13:03.900
Now it is going to be 8; there is 1 less marble in the bag.
00:13:03.900 --> 00:13:07.000
Now we multiply these numbers.
00:13:07.000 --> 00:13:14.800
It is going to be... 1 times 4 is 4; over... 3 times 8 is 24.
00:13:14.800 --> 00:13:19.500
This can be simplified; 4 goes into both numbers.
00:13:19.500 --> 00:13:26.200
Divide each number by 4; this is 1; this is 6.
00:13:26.200 --> 00:13:43.700
The probability of picking a red and then picking a second marble blue without replacing marbles is going to be 1/6.
00:13:43.700 --> 00:13:45.600
Let's go over some examples.
00:13:45.600 --> 00:13:51.400
Determine if the two events are independent or dependent events.
00:13:51.400 --> 00:13:55.100
The first one, rolling a number cube twice.
00:13:55.100 --> 00:14:03.400
Remember for independent or dependent events, we have to have two events; at least two.
00:14:03.400 --> 00:14:06.500
Here rolling a number cube twice.
00:14:06.500 --> 00:14:10.600
The first event would be the first time you roll the number cube.
00:14:10.600 --> 00:14:17.400
The second event is going to be the second time you roll the number cube.
00:14:17.400 --> 00:14:24.900
Does the second event depend on the outcome of the first event?
00:14:24.900 --> 00:14:30.200
Meaning if we roll a number cube, if we roll a die,
00:14:30.200 --> 00:14:36.600
we get either 1 through 6, a number from 1 to 6.
00:14:36.600 --> 00:14:43.500
If you roll it again the second time, does it change or is it affected?
00:14:43.500 --> 00:14:51.800
If I roll a 2 the first time, does that mean I can't roll a 2 the second time?
00:14:51.800 --> 00:14:56.100
The first time we roll a number cube, all the numbers...
00:14:56.100 --> 00:14:59.500
let's say I want to find the probability of picking a 5.
00:14:59.500 --> 00:15:04.600
How many 5s are there?--how many sides on the number cube is a 5?
00:15:04.600 --> 00:15:09.500
There is only 1 side; it will be 1/6.
00:15:09.500 --> 00:15:14.400
That would be the probability of my first roll.
00:15:14.400 --> 00:15:22.600
Then for my second roll, what is the probability of picking a 5 or picking any number?
00:15:22.600 --> 00:15:30.000
It is also 1; do the number of sides change?--no, still the same.
00:15:30.000 --> 00:15:35.700
This roll and this roll, my second roll, they don't affect each other.
00:15:35.700 --> 00:15:37.700
They have nothing to do with each other.
00:15:37.700 --> 00:15:46.100
In this case, this would be independent.
00:15:46.100 --> 00:15:54.000
The second one, drawing a card from a deck of cards and without replacing it, drawing another card.
00:15:54.000 --> 00:15:58.000
There are 52 cards in a deck.
00:15:58.000 --> 00:16:09.500
If I pull a number out or take a card, my total number of cards is going to be 52.
00:16:09.500 --> 00:16:16.300
If I don't put it back in, then for my second draw,
00:16:16.300 --> 00:16:20.900
when I draw my second card, my total is going to be different.
00:16:20.900 --> 00:16:26.000
My probability will be different because it is always desired outcome over the total.
00:16:26.000 --> 00:16:30.900
For my second draw, there is less cards in the deck.
00:16:30.900 --> 00:16:42.900
In this case, this would be dependent because the second draw depends on the first draw.
00:16:42.900 --> 00:16:55.300
The outcome of the second is affected by the first; dependent.
00:16:55.300 --> 00:17:02.600
Picking two students in your class to be class representatives.
00:17:02.600 --> 00:17:11.000
Imagine your class; there is let's say 30 students in the class.
00:17:11.000 --> 00:17:16.200
You pick the first student.
00:17:16.200 --> 00:17:21.300
Let's say you are picking the president and vice-president as class representatives.
00:17:21.300 --> 00:17:25.500
If you pick the first student to be your president,
00:17:25.500 --> 00:17:32.000
how many students do you have left to pick from when you pick the vice-president?
00:17:32.000 --> 00:17:34.700
The total number of students, does it change?
00:17:34.700 --> 00:17:39.900
It does change because you already picked one student and that same person can't be both.
00:17:39.900 --> 00:17:46.300
You pick one student to be the president of your class.
00:17:46.300 --> 00:17:53.900
Then for the vice-president, you have one less student to pick from.
00:17:53.900 --> 00:18:05.600
You have 29 students; so this is dependent; this is dependent.
00:18:05.600 --> 00:18:14.200
These two events would be considered dependent events.
00:18:14.200 --> 00:18:20.000
Samantha rolls a number cube twice; find the probability of each pair of events.
00:18:20.000 --> 00:18:28.600
Here rolling twice, two events, this is the first event; this is the second event.
00:18:28.600 --> 00:18:40.400
We want to know the probability of rolling a 2 and then probability of rolling a 5 afterwards.
00:18:40.400 --> 00:19:08.400
Probability of picking a 2; a number cube... let's say 1 here; 2 here; let's say 5 here.
00:19:08.400 --> 00:19:14.000
There is 6 total sides; how many sides have 2?
00:19:14.000 --> 00:19:18.700
Only 1 side does; my desired outcome is the 2.
00:19:18.700 --> 00:19:21.500
But how many 2s are there?--only 1.
00:19:21.500 --> 00:19:28.900
It is 1 out of a total 6.
00:19:28.900 --> 00:19:34.300
What is the probability for my second roll, for my second event, probability of rolling a 5?
00:19:34.300 --> 00:19:37.200
Again there is only 1 side with a 5.
00:19:37.200 --> 00:19:45.000
1 over... still number of sides is the same, 6.
00:19:45.000 --> 00:19:49.000
The probability of rolling both of those, I just have to multiply
00:19:49.000 --> 00:19:54.900
probability of 2 times the probability of 5 occurring.
00:19:54.900 --> 00:20:01.800
It is going to be 1/6 times 1/6.
00:20:01.800 --> 00:20:07.400
1 times 1; 6 times 6 is 36.
00:20:07.400 --> 00:20:15.800
The probability of rolling a 2 and then rolling a 5 afterwards is 1/36.
00:20:15.800 --> 00:20:25.500
This one here, the probability of rolling a number that is not a 3.
00:20:25.500 --> 00:20:35.800
Probability of not 3; that is my desired outcome; not 3.
00:20:35.800 --> 00:20:39.700
How many numbers are not 3?
00:20:39.700 --> 00:20:45.300
We have 6 of them; only 1 is a 3; the rest aren't.
00:20:45.300 --> 00:20:51.900
There is 5 sides that are not 3; that is going to be 5 on the top.
00:20:51.900 --> 00:21:00.100
Over... how many do I have total?--6.
00:21:00.100 --> 00:21:01.800
That is my first roll; that is my first event.
00:21:01.800 --> 00:21:06.800
My second event, my second roll, is probability of rolling a 6.
00:21:06.800 --> 00:21:13.900
Again there is only 1 side with a 6; that is 1/6.
00:21:13.900 --> 00:21:21.200
Probability of the first one times the probability of the second one.
00:21:21.200 --> 00:21:28.600
Probability of that is 5/6 times probability of the second one 1/6.
00:21:28.600 --> 00:21:43.700
5 times 1 is 5; over 36; that can't be simplified; that is my answer.
00:21:43.700 --> 00:21:50.600
Here we have a spinner that we are going to use to find the probability of each.
00:21:50.600 --> 00:21:57.200
The first one, I only have one event, only 1 spin.
00:21:57.200 --> 00:22:03.800
I am looking for the probability of rolling a black; there are no blacks.
00:22:03.800 --> 00:22:12.400
It is red, orange, yellow, green, blue, purple, light purple, and then another orange.
00:22:12.400 --> 00:22:17.000
Probability of rolling a black, my desired outcome is black.
00:22:17.000 --> 00:22:22.700
Do I have any black?--no; 0 on top.
00:22:22.700 --> 00:22:34.300
Over... how many total do I have?--1, 2, 3, 4, 5, 6, 7, 8; over 8.
00:22:34.300 --> 00:22:37.900
This 0/8 is always 0.
00:22:37.900 --> 00:22:44.500
If have a 0 on top, that is going to make the whole thing 0.
00:22:44.500 --> 00:22:52.100
Here there is no probability of picking a black; that is what the 0 means.
00:22:52.100 --> 00:22:58.000
For the second one, we want to know the probability of spinning a red.
00:22:58.000 --> 00:23:03.700
And then if we do a second spin, because there is two events...
00:23:03.700 --> 00:23:08.200
First spin lands on red; second spin lands on green.
00:23:08.200 --> 00:23:17.300
Probability of red; how many sections of red do I have?
00:23:17.300 --> 00:23:26.300
I only have 1; 1 over... total number of sections, 8.
00:23:26.300 --> 00:23:30.600
What about probability of green?
00:23:30.600 --> 00:23:40.000
This would be considered independent events because if I spin the first time, I land on red.
00:23:40.000 --> 00:23:45.100
That is not going to affect what my second spin is going to land on.
00:23:45.100 --> 00:23:53.100
These would be independent; the probability of green is 1 out of 8.
00:23:53.100 --> 00:24:00.100
I multiply them together; 1/8 times 1/8.
00:24:00.100 --> 00:24:08.400
1 times 1 is 1; 8 times 8 is 64.
00:24:08.400 --> 00:24:15.700
The probability of landing on red and then spinning again landing on green is 1/64.
00:24:15.700 --> 00:24:24.100
The next one, the probability of landing on any color that is not yellow
00:24:24.100 --> 00:24:28.100
and then for the second spin, landing on blue.
00:24:28.100 --> 00:24:35.000
Probability of not yellow; how many are not yellow?
00:24:35.000 --> 00:24:44.600
There is 8; there is only 1 yellow; 7 are not yellow; 7/8.
00:24:44.600 --> 00:24:52.500
The probability of blue; there is 1 blue; 1/8.
00:24:52.500 --> 00:25:05.300
We are going to multiply them together; 7/8 times 1/8 is 7/64.
00:25:05.300 --> 00:25:19.400
If you notice these two numbers, the chances of this happening is greater than the chances of this happening
00:25:19.400 --> 00:25:29.300
because here the chances of the spinner landing on a color that is not yellow is actually pretty high.
00:25:29.300 --> 00:25:37.400
7/8, that is pretty high because there is so many spaces that are not yellow.
00:25:37.400 --> 00:25:40.800
If this fraction is greater than this fraction, that means
00:25:40.800 --> 00:25:50.200
the probability of this happening is greater than the chances of that happening.
00:25:50.200 --> 00:26:00.300
For our fourth example, we have a bag of marbles; draw my bag of marbles.
00:26:00.300 --> 00:26:06.400
I have 5 red marbles; 1, 2, 3, 4, 5.
00:26:06.400 --> 00:26:11.800
I have 4 blue; 1, 2, 3, 4.
00:26:11.800 --> 00:26:15.500
I have 6 green; I don't have green color.
00:26:15.500 --> 00:26:26.300
I am going to use black G for green; 1, 2, 3, 4, 5, 6.
00:26:26.300 --> 00:26:33.200
We are going to find the probability for each when the first marble is not replaced back in the bag.
00:26:33.200 --> 00:26:36.200
Here we have two events; two things are happening.
00:26:36.200 --> 00:26:40.900
We are going to pick two marbles.
00:26:40.900 --> 00:26:46.500
After you pick the first marble, we are not going to put it back in the bag.
00:26:46.500 --> 00:26:48.800
It is not going to be replaced back in.
00:26:48.800 --> 00:26:52.400
We pick one; that one stays out of the bag.
00:26:52.400 --> 00:26:58.400
Then we are going to pick our second marble; that is my two events.
00:26:58.400 --> 00:27:06.200
Remember the second event, because after we pick the first marble, we are not going to replace it back in.
00:27:06.200 --> 00:27:13.100
That is going to affect the probability of that second marble.
00:27:13.100 --> 00:27:25.600
Both of these would be considered dependent events because the second one is affected by that first event.
00:27:25.600 --> 00:27:31.900
Let's first talk about this event, the probability of picking a green.
00:27:31.900 --> 00:27:36.200
That is our first pick, green.
00:27:36.200 --> 00:27:41.600
Probability, we look at the desired outcome over the total possible number of outcomes.
00:27:41.600 --> 00:27:49.700
How many green marbles do I have?--I have 1, 2, 3, 4, 5, 6.
00:27:49.700 --> 00:27:52.500
6 is going to be my top number.
00:27:52.500 --> 00:27:56.500
Over... how many marbles do I have total, in all?
00:27:56.500 --> 00:28:02.700
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15.
00:28:02.700 --> 00:28:11.100
That is going to go right there; the probability of picking a green is 6/15.
00:28:11.100 --> 00:28:13.800
It is still a fraction; I still have to simplify it.
00:28:13.800 --> 00:28:21.800
What number goes into both 6 and 15?--they share a factor of 3.
00:28:21.800 --> 00:28:30.400
This is going to be 2/5; the probability of picking a green is 2/5.
00:28:30.400 --> 00:28:38.900
Now I have to pick my second marble; that is going to be red.
00:28:38.900 --> 00:28:47.300
Because that first marble was not replaced back in the bag, this marble, one of the green, is now gone.
00:28:47.300 --> 00:28:52.200
It is no longer in there.
00:28:52.200 --> 00:28:55.100
Probability of picking the red, how many reds to I have?
00:28:55.100 --> 00:28:59.100
I have 5 red marbles; 5 on top.
00:28:59.100 --> 00:29:02.900
Over... how many marbles do I have now?
00:29:02.900 --> 00:29:08.500
After that 1 is gone, I have 14 left.
00:29:08.500 --> 00:29:12.800
It was 15 and then minus the 1 that we have already picked.
00:29:12.800 --> 00:29:18.500
Now it is 5/14; this fraction I can't simplify.
00:29:18.500 --> 00:29:21.500
That is the probability of picking the red.
00:29:21.500 --> 00:29:29.100
Now to find the probability of both happening, I take this one and I take this one; I multiply it together.
00:29:29.100 --> 00:29:39.800
It will be probability of the green times the probability of picking the red.
00:29:39.800 --> 00:29:52.300
This is dependent; it is the red after green; 2/5 times 5/14.
00:29:52.300 --> 00:29:59.400
2 times 5 is 10; 5 times 14; 14 times 5.
00:29:59.400 --> 00:30:09.200
We do this; that is 20; 5 times 1 plus the 2 is 70.
00:30:09.200 --> 00:30:13.700
Fraction, I have to simplify it; what number goes into both top and bottom?
00:30:13.700 --> 00:30:21.900
10; I divide by 10 for each; I get 1/7 as my answer.
00:30:21.900 --> 00:30:25.300
The probability of picking a green and then afterwards
00:30:25.300 --> 00:30:33.800
without replacing it back in, picking a red marble, is 1/7.
00:30:33.800 --> 00:30:42.300
I need to write this for this second problem.
00:30:42.300 --> 00:30:45.100
Now we want to find the probability of picking a blue
00:30:45.100 --> 00:30:50.700
and then afterwards without replacing it back in, pick another blue.
00:30:50.700 --> 00:30:55.100
Again two dependent events.
00:30:55.100 --> 00:31:04.600
Probability of picking the first blue, the first event, what is my desired outcome?
00:31:04.600 --> 00:31:06.400
How many blue marbles do I have here in the bag?
00:31:06.400 --> 00:31:14.200
I have 4 blue over a total of 15 marbles.
00:31:14.200 --> 00:31:17.800
The probability of picking a blue marble is 4/15.
00:31:17.800 --> 00:31:21.500
I can't simplify it; so that is the probability.
00:31:21.500 --> 00:31:30.800
For my second pick, because again it is not being replaced in the bag.
00:31:30.800 --> 00:31:36.600
This one is no longer in the bag; I have 1 less marble.
00:31:36.600 --> 00:31:43.900
For my second pick, I want to look at how many blue marbles I have left.
00:31:43.900 --> 00:31:52.900
I have 3 left; I had 4 but 1 is gone; now I have 3.
00:31:52.900 --> 00:32:02.100
Over... I don't have 15 anymore; I have 14 now.
00:32:02.100 --> 00:32:05.600
Probability of picking the first blue was 4 out of 15
00:32:05.600 --> 00:32:13.000
because I had all my blue, just 4 of them, out of a total of 15 marbles.
00:32:13.000 --> 00:32:17.400
For my second pick, I am also wanting to pick another blue one.
00:32:17.400 --> 00:32:21.100
I only have 3 left because the first one wasn't replaced back in.
00:32:21.100 --> 00:32:24.700
Out of a total of 14 marbles left.
00:32:24.700 --> 00:32:31.200
Now I am going to take the first event and then
00:32:31.200 --> 00:32:35.800
multiply it to the probability of the second event happening.
00:32:35.800 --> 00:32:42.500
It is 4/15 times 3/14.
00:32:42.500 --> 00:32:51.000
4 times 3 is 12; over... 15 times 14; you are going to multiply it.
00:32:51.000 --> 00:32:58.000
This is 20; that is 4 times 1 is 4; plus 2 is 6.
00:32:58.000 --> 00:33:03.600
I leave the space alone; 1 times 5 is 5; 1 times 1 is 1.
00:33:03.600 --> 00:33:18.300
I am going to add them down; 0; this is 11; this is 2; 210.
00:33:18.300 --> 00:33:27.000
I know I can simplify this fraction because this number is an even number and this number is an even number.
00:33:27.000 --> 00:33:40.200
Let's divide each of these by 2; 12 divided by 2 is 6.
00:33:40.200 --> 00:33:52.000
Over... this, if I take the 200 and I divide it by 2, I get 100.
00:33:52.000 --> 00:33:56.700
This divided by 2 is 100; this divided by 2 is 5.
00:33:56.700 --> 00:34:06.000
If I divide the whole thing, it will be 105.
00:34:06.000 --> 00:34:11.400
It looks like 6/105; I also have another factor.
00:34:11.400 --> 00:34:19.600
I can divide this again by... I know 3 goes into that one and 3 also goes into this one.
00:34:19.600 --> 00:34:25.000
6 divided by 3 is... write it down here... 2.
00:34:25.000 --> 00:34:33.200
Over... 105 divided by 3; let me show you that one.
00:34:33.200 --> 00:34:37.000
3 goes into 10 three times; that gives you a 9.
00:34:37.000 --> 00:34:42.200
Subtract it; I get 1 left over; bring down the 5.
00:34:42.200 --> 00:34:48.000
3 goes into 15 five times; that gives you 15.
00:34:48.000 --> 00:34:55.000
We subtract it; I have no remainders; my answer is 35.
00:34:55.000 --> 00:35:00.200
Can I simplify this further?--no, I can't because this is not an even number.
00:35:00.200 --> 00:35:02.600
This is my answer.
00:35:02.600 --> 00:35:11.500
Again finding the probability of two events, you have to find the probability of each event occurring.
00:35:11.500 --> 00:35:16.500
Then you are going to multiply them together, whether it is independent or dependent events.
00:35:16.500 --> 00:35:19.000
That is it for this lesson; thank you for watching Educator.com.