WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com; for the next lesson, we are going to go over probability.
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Probability is the measure of an outcome compared to the total possible number of outcomes.
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It is in the form of a fraction.
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That means we are going to have a top number and we are going to have a bottom number.
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We are going to have a numerator and denominator.
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On the top, you are going to write the number of the desired outcome.
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Basically what are you looking for?--what is it asking for?
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That number is going to go on the top.
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Then on the bottom, you are going to write the total number of possible outcomes.
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Probability is the measure between the part, the part that you want
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or the part that it is asking for over the whole thing or the total.
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That is the ratio; the ratio is between the part to the whole.
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For example, if I have a bag full of marbles, let's say I have one black marble in this bag.
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I have 3 blue marbles; and I have 2 red marbles.
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I want to know what is the probability, what are the chances of picking a blue marble?
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If I close my eyes and reach into the bag and pick one marble,
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what is the probability, what are the chances of picking a blue marble?
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That would be the number of blue marbles is going to go on the top.
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Blue marbles over... remember the bottom is always the total number, the total number of marbles.
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This is going to be my probability.
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How many blue marbles do I have?
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I have 3; that is my desired outcome.
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I am asking you what are the chances of me picking a blue?
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There are 3 blue marbles; it is going to be 3 on the top.
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Over... how many marbles do I have in all?
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1, 2, 3, 4, 5, 6; 6; my probability is 3/6.
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Since this is a fraction, I need to simplify it.
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If 3/6, then I have to divide this by 3, divide this by 3.
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This becomes 1; 6 divided by 3 is 2.
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The probability of picking a blue marble from this bag of marbles is 1 to 2 or 1/2.
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Let's go over some examples.
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The first example, what is the probability of landing on orange?
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Here I have a pie chart that is divided up into 1, 2, 3, 4, 5 different colors.
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Orange, purple, yellow, green, red; what is the probability...
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If I spin this spinner, what is the probability of landing on orange?
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That means orange is my desired outcome; that is what I am asking for.
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The orange is going to go on the top.
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The total or the whole thing is going to go on the bottom.
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How many orange sections do I have?--I only have 1.
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Then I am going to put 1 on the top.
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How many different sections do I have?--1, 2, 3, 4, 5.
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Out of 5 sections, 1 of them is orange.
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That is why the top number is 1.
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On the bottom, I am going to put 5 because that is the total.
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The probability of landing on orange is going to be 1/5.
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Again it is part to whole; so 1 to 5 is the probability.
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If I ask you what is the probability of landing on purple?
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There is 1 purple out of total of 5 different colors.
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It will be the same thing, 1/5.
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The next example, each side of a dice has a number from 1 to 6.
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What is the probability of rolling a 5?
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We know what a dice is; it is a cube that looks like this.
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Each side has a number representing dots usually.
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One side will have 1; the other side will have maybe 2.
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One side will have 3; another side might have 4 like that.
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There are 6 sides; each side has a different number of dots.
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I want to know what the probability of rolling a 5 is.
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The desired outcome, the top number is going to be rolling a 5.
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Then the bottom number is going to just be the total or the total number of numbers.
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Even though this is a number, that is not the actual number I am going to write on the top for my probability
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because there is not 5 of something; there is not five 5s.
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How many 5s do I have on this?--how many sides have 5 dots?
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Only 1 because each side has a different number.
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There is only one side that will have 5 dots.
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That means I have to put 1 here because it is the number of this desired outcome.
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It is not what this number is.
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It is not that this is a 5 and I have to write the 5 up here.
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It is how many sides do I have with 5 dots?--that is just 1.
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How many total number of sides do I have?--6.
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because again when you are rolling a dice, you are looking to see what the top side is going to be.
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How many dots is the top side going to have?
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That is 1 out of 6.
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Same thing if I asked you what is the probability of rolling a 2?
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Isn't this roll a 2 right now?
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How many sides have a 2?--only one side does.
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It will be the same thing, 1 out of a 6 possible sides.
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1/6 is the probability.
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More marbles; there are 2 red marbles, 5 blue marbles, and 3 green marbles in the bag.
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Let me draw my bag; I have 2 red; red, red.
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I have 5 blue; 1, 2, 3, 4, 5; blue, blue, blue, blue, blue.
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I have 3 green; 1, 2, 3; green, green, green.
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What is the probability that the marble will be red?
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That is my desired outcome; that is the part that is asked for.
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That is going to go on the top; red over total; that is my probability.
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How many reds do I have?--I have... it says here 2 red; red and red.
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2 out of... how many do I have in all?--1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10 total marbles.
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My probability would be 2 out of 10.
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Again this is still a fraction; I have to simplify it.
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I know that because the top number and the bottom number are both even numbers,
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I can divide both of them by a 2.
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2/10 becomes... 2 divided by 2 is 1; over... 10 divided by 2 is 5.
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The probability of picking a red is 1 out of 5.
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The fourth example, there are 6 boys and 5 girls in a room.
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If one student is chosen at random, what is the probability that the student will be a girl?
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Again my desired outcome, girl over total.
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I now that there are 5 girls; number of girls is going to be 5.
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On the bottom, I am not writing the number of boys.
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Be careful with this type of example because when it comes to ratio which we learned a few lessons ago,
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if I ask for the ratio of girls to boys, then I would put 5 on the top and 6 on the bottom
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because that would represent girls to boys.
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But this is probability; this is girls to total number of students.
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The bottom number for probability is always the total.
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How many students do I have in all?--5 out of how many in all?
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I would have to add the number of boys and the number of girls
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to figure out how many total number of students there are.
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If I have 6 boys and 5 girls, then I have 11 students in all.
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The total I am going to write is 11.
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Girls, 5; there is 5 girls; out of 11 students.
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The probability is 5/11; this is the probability.
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If they ask for the ratio of girls to boys, then it would be 5 to 6.
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But again probability is different; total number has to go on the bottom.
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That is it for this lesson; thank you for watching Educator.com.