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Post by Ramez Hajelsawi on March 27, 2013

i know this

Probability

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  • Probability: the measure of an outcome to the total possible outcomes
  • Probabilities are often in the form of a fraction
  • The top of the fraction is the number of the desired outcome
  • the bottom of the fraction is the total number of possible outcomes

Probability

Each side of a dice has a number from 1 to 6. What is the probability of rolling a 4
[1/6]
Each side of a dice has a number from 1 to 6. What is the probability of rolling a 1
[1/6]
Each side of a dice has a number from 1 to 6. What is the probability of rolling a 7
0
There are 3 red marbles, 6 blue marbles, and 3 green marbles in a bag. If I reach in and grab one marble, what is the probability that the marble will be red?
  • Total marbles = 3 + 6 + 3 = 12
  • [red/total]
  • [(3 ÷3)/(12 ÷3)] = [1/4]
[1/4]
There are 4 red marbles, 10 blue marbles, and 6 green marbles in a bag. If I reach in and grab one marble, what is the probability that the marble will be blue?
  • Total = 4 + 10 + 6 = 20
  • [blue/total] = [10/20]
  • [(10 ÷10)/(20 ÷10)] = [1/2]
[1/2]
There are 12 boys and 8 girls in the room. If one student is chosen at random, what is the probability that the student will be a girl?
  • Total students = 12 + 8 = 20
  • [girls/total] = [8/20]
  • [(8 ÷4)/(20 ÷4)]
[2/5]
There are 30 boys and 17 girls in the room. If one student is chosen at random, what is the probability that the student will be a girl?
  • Total students = 30 + 17 = 47
  • [girls/total] = [17/47]
[17/47]
There are 7 red pens, 11 blue pens, and 3 green pens in a box. If I reach in and grab one pen, what is the probability that the pen will be green?
  • Total = 7 + 11 + 3 = 21
  • [green/total] = [3/21]
  • [(3 ÷3)/(21 ÷3)]
[1/7]
There are 9 red pens, 15 blue pens, 3 green pens, and 12 yellow pens in a box. If I reach in and grab one pen, what is the probability that the pen will be green?
  • Total = 9 + 15 + 3 + 12 = 39
  • [green/total] = [3/39]
  • [(3 ÷3)/(39 ÷3)]
[1/13]
There are 13 red pens, 12 blue pens, 11 green pens, and 14 yellow pens in a box. If I reach in and grab one pen, what is the probability that the pen will be yellow?
  • Total = 13 + 12 + 11 + 14 = 50
  • [yellow/total] = [14/50]
  • [(14 ÷2)/(50 ÷2)]
[7/25]

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Probability

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Probability 0:05
    • Introduction to Probability
    • Example: Probability
  • Extra Example 1: What is the Probability of Landing on Orange? 3:26
  • Extra Example 2: What is the Probability of Rolling a 5? 5:02
  • Extra Example 3: What is the Probability that the Marble will be Red? 7:40
  • Extra Example 4: What is the Probability that the Student will be a Girl? 9:43

Transcription: Probability

Welcome back to Educator.com; for the next lesson, we are going to go over probability.0000

Probability is the measure of an outcome compared to the total possible number of outcomes.0007

It is in the form of a fraction.0015

That means we are going to have a top number and we are going to have a bottom number.0018

We are going to have a numerator and denominator.0021

On the top, you are going to write the number of the desired outcome.0026

Basically what are you looking for?--what is it asking for?0038

That number is going to go on the top.0041

Then on the bottom, you are going to write the total number of possible outcomes.0045

Probability is the measure between the part, the part that you want0060

or the part that it is asking for over the whole thing or the total.0066

That is the ratio; the ratio is between the part to the whole.0073

For example, if I have a bag full of marbles, let's say I have one black marble in this bag.0085

I have 3 blue marbles; and I have 2 red marbles.0096

I want to know what is the probability, what are the chances of picking a blue marble?0114

If I close my eyes and reach into the bag and pick one marble,0122

what is the probability, what are the chances of picking a blue marble?0126

That would be the number of blue marbles is going to go on the top.0133

Blue marbles over... remember the bottom is always the total number, the total number of marbles.0138

This is going to be my probability.0150

How many blue marbles do I have?0153

I have 3; that is my desired outcome.0155

I am asking you what are the chances of me picking a blue?0157

There are 3 blue marbles; it is going to be 3 on the top.0162

Over... how many marbles do I have in all?0167

1, 2, 3, 4, 5, 6; 6; my probability is 3/6.0170

Since this is a fraction, I need to simplify it.0179

If 3/6, then I have to divide this by 3, divide this by 3.0183

This becomes 1; 6 divided by 3 is 2.0190

The probability of picking a blue marble from this bag of marbles is 1 to 2 or 1/2.0194

Let's go over some examples.0204

The first example, what is the probability of landing on orange?0208

Here I have a pie chart that is divided up into 1, 2, 3, 4, 5 different colors.0214

Orange, purple, yellow, green, red; what is the probability...0223

If I spin this spinner, what is the probability of landing on orange?0227

That means orange is my desired outcome; that is what I am asking for.0234

The orange is going to go on the top.0239

The total or the whole thing is going to go on the bottom.0245

How many orange sections do I have?--I only have 1.0251

Then I am going to put 1 on the top.0256

How many different sections do I have?--1, 2, 3, 4, 5.0260

Out of 5 sections, 1 of them is orange.0266

That is why the top number is 1.0269

On the bottom, I am going to put 5 because that is the total.0272

The probability of landing on orange is going to be 1/5.0275

Again it is part to whole; so 1 to 5 is the probability.0281

If I ask you what is the probability of landing on purple?0289

There is 1 purple out of total of 5 different colors.0292

It will be the same thing, 1/5.0297

The next example, each side of a dice has a number from 1 to 6.0304

What is the probability of rolling a 5?0310

We know what a dice is; it is a cube that looks like this.0313

Each side has a number representing dots usually.0322

One side will have 1; the other side will have maybe 2.0330

One side will have 3; another side might have 4 like that.0334

There are 6 sides; each side has a different number of dots.0341

I want to know what the probability of rolling a 5 is.0350

The desired outcome, the top number is going to be rolling a 5.0354

Then the bottom number is going to just be the total or the total number of numbers.0363

Even though this is a number, that is not the actual number I am going to write on the top for my probability0371

because there is not 5 of something; there is not five 5s.0378

How many 5s do I have on this?--how many sides have 5 dots?0382

Only 1 because each side has a different number.0389

There is only one side that will have 5 dots.0393

That means I have to put 1 here because it is the number of this desired outcome.0397

It is not what this number is.0403

It is not that this is a 5 and I have to write the 5 up here.0406

It is how many sides do I have with 5 dots?--that is just 1.0409

How many total number of sides do I have?--6.0417

because again when you are rolling a dice, you are looking to see what the top side is going to be.0422

How many dots is the top side going to have?0429

That is 1 out of 6.0433

Same thing if I asked you what is the probability of rolling a 2?0437

Isn't this roll a 2 right now?0441

How many sides have a 2?--only one side does.0445

It will be the same thing, 1 out of a 6 possible sides.0449

1/6 is the probability.0455

More marbles; there are 2 red marbles, 5 blue marbles, and 3 green marbles in the bag.0464

Let me draw my bag; I have 2 red; red, red.0475

I have 5 blue; 1, 2, 3, 4, 5; blue, blue, blue, blue, blue.0484

I have 3 green; 1, 2, 3; green, green, green.0494

What is the probability that the marble will be red?0503

That is my desired outcome; that is the part that is asked for.0506

That is going to go on the top; red over total; that is my probability.0513

How many reds do I have?--I have... it says here 2 red; red and red.0522

2 out of... how many do I have in all?--1, 2, 3, 4, 5, 6, 7, 8, 9, 10.0534

1, 2, 3, 4, 5, 6, 7, 8, 9, 10 total marbles.0544

My probability would be 2 out of 10.0550

Again this is still a fraction; I have to simplify it.0554

I know that because the top number and the bottom number are both even numbers,0560

I can divide both of them by a 2.0563

2/10 becomes... 2 divided by 2 is 1; over... 10 divided by 2 is 5.0568

The probability of picking a red is 1 out of 5.0577

The fourth example, there are 6 boys and 5 girls in a room.0585

If one student is chosen at random, what is the probability that the student will be a girl?0592

Again my desired outcome, girl over total.0601

I now that there are 5 girls; number of girls is going to be 5.0611

On the bottom, I am not writing the number of boys.0620

Be careful with this type of example because when it comes to ratio which we learned a few lessons ago,0623

if I ask for the ratio of girls to boys, then I would put 5 on the top and 6 on the bottom0630

because that would represent girls to boys.0637

But this is probability; this is girls to total number of students.0640

The bottom number for probability is always the total.0647

How many students do I have in all?--5 out of how many in all?0652

I would have to add the number of boys and the number of girls0658

to figure out how many total number of students there are.0662

If I have 6 boys and 5 girls, then I have 11 students in all.0666

The total I am going to write is 11.0674

Girls, 5; there is 5 girls; out of 11 students.0677

The probability is 5/11; this is the probability.0685

If they ask for the ratio of girls to boys, then it would be 5 to 6.0692

But again probability is different; total number has to go on the bottom.0702

That is it for this lesson; thank you for watching Educator.com.0707