What are the chances?

Sample Space

1

This is the definition of sample space.

What is all the possible outcomes of a scenario?

2

This is the sample space for a bag of marbles, with 2 red marbles, and 1 blue marble.

What is S = {R, R, B}

3

This is the sample space for two dice, both are D4s.

What is ?

4

This is the sample space for a bag of marbles with 3 red, 2 blue, and 1 green. You choose a marble, replace it, and choose again.

Independent VS Dependent

1

Provide an example of an independent event.

What is multiple possible answers... IMPORTANT PART is replacement if it's a draw and then redraw.

2

Determine if the following scenario is an independent or dependent event: Lawrence has two dice, one is a D6, the other is a D20. Lawrence rolls the D6 first, then the D20.

What is independent? The outcome of the D6 DOES NOT influence the outcome of the D20.

3

Determine if the following scenario is an independent or dependent event: Barry has a bag of 25 slips of paper with 5 different names, 5 slips for each name. He is going to pick the girl that he wants to go out to homecoming with; and the girl he wants to go to the afterparty with. He picks a name out of the bag, puts it to the side, and then picks again.

What is dependent event? Barry (the scumbag he is) is changing the outcomes of the events from the first pull, to the second pull. They are not the same.

4

Determine if the following scenario is an independent or dependent event: Johann has 20 instruments to create a musical piece with. He puts the names of the instruments into a hat, pulls a name out, then without replacement, pulls another, then repeats the process 4 more times.

What is dependent event? There are less slips in the bag each time, resulting in a smaller and smaller fraction denominator with each pull of a name. Each pull affects the outcome of the following pull.

Conditional Probability

1

Determine if this is a conditional probability problem: Edgar is hungry for cookies, he goes to pull a cookie out of the cookie jar, where there are 10 chocolate chip cookies, 5 oatmeal raisin cookies, and 12 peanut butter cookies; Edgar pulls a cookie out, eats it, and then repeats the process 3 times.

What is this is a conditional probability problem? The events of the first cookie Edgar eats changes the probability of the cookie choices of the second cookie he pulls.

2

This is the probability (Represented as a fraction, decimal and percent) that a student has a cat given that they do not have a dog. 

What is 4/11, 0.3636, and 36.36%?

3

Determine the probability if a resident who has a master's degree is chosen at random, that they are aged 50 or over. 

What is  909/2620 

4

If P(A)= 0.43, P(B)= 0.32, and 

P(AnnB)=0.08

Find 

P(AuuB)=

and

P(B|A)=

What is  P(AuuB)=0.67 

P(B|A)=0.186

Two Way Tables

1

This is the probability that a student chosen randomly from the class completed the homework.

What is 21/27?

2

This is the probability that a student chosen randomly from the class failed the test and did not complete the homework.

What is 2/7? Simplified from 6/21.

3

This is the probability that a student who does not have a brother has a sister. 

What is 5/13?

4

When a resident who is 40 or older is chosen at random, this is the probability that they have only completed high school. 

What is 1657/8545?

Have completed high school: 729+928=1657

Age 40 or older: 3326+5219=8545

Compound Probability

1

A bag contains 4 red marbles, 2 blue marbles and 3 green marbles, this is the probability when two marbles are drawn out of the bag that both marbles drawn will be green.

What is 1/12?

1st Draw 3/9

2nd Draw 2/8

3/9⋅2/8=6/72=1/12

2

A bag contains 5 red marbles, 6 blue marbles and 4 green marbles. This is the probability if three marbles are drawn out of the bag, and they are all blue marbles.

What is 2/45?

P(Blue on first draw)=6/15

P(Blue on second draw)=5/14

P(Blue on third draw)=4/13

Compound Event: Multiply Probabilities

6/15⋅5/14⋅4/13=120/2730 = 12/273 = 2/45

3

Given  P(AuuB)=0.5, P(A)=0.8, andP(AnnB)=0.4)Find 

 P(B) 

What is 0.1?

4

Given  P(AnnB)=0.2,P(B)=0.7, P(A)=0.24 Find  P(A|B)=, P(AuuB)= 

What is 

P(A|B)=0.286, P(AuuB)=0.74

Addition, Multiplication, Permutations, Combinations

1

There is a spinner with 8 equal areas, numbered 1 through 8. This is the probability when the spinner is spun one time, that the result is a multiple of 3 or a multiple of 2.

What is 5/8?

2

This is the amount of outfits you can make with 6 shorts and 12 shirts

What is 72 outfits?

3

There is a spinner with 12 equal areas, numbered 1 through 12. This is the probability when the spinner is spun one time, that the result is a multiple of 3 and a multiple of 4.

What is 1/12?

4

There were 9 students running in a race. This is the amount of different arrangements of first, second, and third place that are possible.

What is 504?

ORDER MATTERS

Arranging 3 people from a group of 9

9P3