Math Studies Probability Review

Venn Diagrams

Tree Diagrams

Conditional Probability

General Probability

Other Topics

100

20 students went to the park. 10 of them wore hats, 12 of them wore jackets, and 3 of them wore both. Represent this situation in a Venn Diagram.

Hats only: 7

Jackets only: 9

Middle: 3

Outside: 1

100

Bob flips 2 fair coins. Repersent this in a tree diagram.

1/2: heads

1/2: tails

1/2: heads

1/2: tails

100

What is the conditional probability formula?

P(A|B)=P(A and B)/P(B)

100

What is the sample space?

Sample space is a list of possible outcomes.

100

p: It is Tuesday.

q: It is raining.

Write in words p V q.

It is Tuesday or it is raining.

200

There are 30 people on a city bus. 20 of them are going to work, 10 of them are wearing slacks, and 5 of them are neither going to work nor wearing slacks. Represent this in a Venn Diagram.

Only work: 15

Only slacks: 5

Work and Slacks: 5

Outside: 5

200

A bag has 2 blue marbles and 5 green marbles. You draw 2 marbles from the bag with replacement. Represent this in a tree diagram.

2/7 blue

5/7 green

2/7 blue

5/7 green

200

In a group of 40 boys, 23 have dark hair, 18 have brown eyes, and 26 have dark hair, brown eyes, or both. One of the boys is selected randomly. Determine the probability that he has brown eyes given that he has dark hair.

P(X)=15/23

P(X)=0.652

200

What does it mean if A and B are independent?

A and B are independent if the outcome of A doesn't affect the probability of B.

200

For Pearson's Correlation Coefficient, how would you describe the strength and direction of r=-0.9?

r=-0.9 is a strong negative correlation

300

A badminton club has 31 playing members. 28 play singles and 16 play doubles. Represent this as a Venn Diagram.

Only singles: 15

Only doubles: 3

Singles and doubles: 13

Outside: 0

300

A bag holds 3 red marbles, 5 yellow marbles, and 2 black marbles. If you grab one marble, replace it, and draw another marble, what is the probability that you draw the same color for both marbles?

P(X)=(3/10)(3/10)+(5/10)(5/10)+(2/10)(2/10)

P(X)=38/100

P(X)=19/50

P(X)=0.38

300

Urn A contains 2 red and 3 blue marbles, and urn B contains 4 red and 1 blue marble. Peter selects an urn by tossing a coin, and takes a marble from that urn. Given that the marble is red, what is the probability that it came from B?

P(X)=(1/2)(4/5)/[(1/2)(2/5)+(1/2)(4/5)]

P(X)=(2/5)/(3/5)

P(X)=6/25

P(X)=0.24

300

You roll two dice. Find the probability that the first is odd and the second is a multiple of 3.

=(3/6)(2/6)

=(1/2)(1/3)

=1/6

300

What is the gradient of the line y=3x+1?

The gradient, or slope, is 3.

400

A survey of 21 farms showed that 15 grow crops, 9 have cattle, and and 11 have sheep. 4 have sheep and cattle, 7 have cattle and crops, and 8 have sheep and crops. 3 have cattle, sheep, and crop. Find the number of farms with only animals.

1+2+1=4

400

You bought 3 tickets for a raffle out of 150. There are 2 prizes that will be drawn for without replacing raffle tickets. Represent your chances of winning these prizes in a tree diagram.

3/150 win

2/149 win

147/149 lose

147/150 lose

3/149 win

146/149 lose

400

The probability Greta's mother takes her shopping is 2/5. When Greta goes shopping with her mother, she gets ice cream 70% of the time. When Greta does not go shopping with her mother she gets ice cream 30% of the time. Determine the probability that Greta went shopping with her mother, given that her mother buys her an ice cream.

P(X)=(2/5)(0.7)/[(2/5)(0.7)+(3/5)(0.3)]

P(X)=0.28/0.46

P(X)=0.609

400

On average, Steve runs 4 days a week. What is the probability that on 3 randomly selected days, Steve ran on all of them?

=(4/7)(4/7)4/7)

=64/343

=0.187

400

The line L₁ has equation y=-2x+1. Find the gradient of the line L₂ which is perpendicular to L₁.

The gradient of L₂ is the opposite reciprocal, 1/2.

500

A bouquet shop is arranging 40 bouquets with red, yellow, and purple flowers. 10 bouquets are using all three colors, 15 are using red and yellow, 11 are using red and purple, and 12 are using yellow and purple. There are 31 with red flowers and 21 with yellow flowers. Find the probability that a randomly selected bouquet has only purple flowers.

40-(10+1+2+5+15+4)=3

P(X)=3/40

500

You have a bag containing 5 purple marbles and 4 yellow marbles. You draw 3 marbles simultaneously. Find the probability that you get at least 1 purple marble.

P(X)=1-(4/9)(3/8)(2/7)

P(X)=1-24/504

P(X)=1-1/21

P(X)=20/21

P(X)=0.952

500

The probability that a randomly selected person has cancer is 0.02. The probability that he or she reacts positively to a test which detects cancer is 0.95 if he or she has cancer, and 0.03 if he or she does not. Determine the probability that a randomly tested person has cancer given that he or she reacts positively.

P(X)=(0.02)(0.95)/[(0.02)(0.95)+(0.98)(0.03)]

P(X)=0.019/0.0484

P(X)=0.393

500

The probability that 3 people score a free throw are 2/5, 1/3, and 1/2 respectively. Find the probability that at least one of them score a free throw.

=1-(3/5)(2/3)(1/2)

=1-6/30

=1-1/5

=4/5

=0.8

500

In triangle ABC, find a if A=63^o, B=49^o, and b=18cm.

a=21.3 cm