# Conditional Probability Word Problems

### Solutions

1If A and B are two random events with probabilities of p(A) = 1/2, p(B) = 1/3, p(A B)= 1/4, calculate:

1

2

3

4

5

2If A and B are two random events with probabilities of p(A) = 1/3, p(B) = 1/4, p(A B) = 1/5, calculate:

1

2

3

4

5

6

3Students in a high school can choose to study Spanish or French as a foreign language. In a given academic year, 90% of the pupils choose Spanish and the rest choose French. 30% of the students who are learning Spanish are boys and 40% who are studying French are also boys. If a student was randomly selected from this academic year, what is the probability that it would be a girl?

4Two cards are removed simultaneously from a deck of 48 cards. Calculate the probability of drawing:

1 Two diamonds.

2At least one diamond.

3One diamond and one heart.

5A student has studied only 15 of the 25 topics covered in a semester for a particular class. For the exam, the student is allowed to randomly select two issues and choose one of the two to write about. Find the probability that the student will choose one of the topics that he has studied.

6A class is formed by 10 boys and 10 girls. Half of the girls and half of the boys have selected French as their optional subject.

1 What is the probability that a randomly selected student is a boy or somebody who studies French?

2What is the probability that a randomly selected student is girl who does not study French?

7A car workshop knows that on an average morning: three cars with electrical problems, eight with mechanical problems and three with sheet metal problems arrive at the shop for service. In the afternoon, two cars with electrical problems, three with mechanical problems and one car with sheet problems also arrive at the shop.

1 Create a table ordering the data.

2Calculate the percentages of the cars who arrive in the afternoon.

3Calculate the percentage of the cars that arrive with mechanical problems.

4Calculate the probability that a car with electrical problems will arrive in the morning.

8A class consists of six girls and ten boys. If a committee of three is chosen at random, find the probability of:

1 Three boys being selected.

2Exactly two boys and a girl being selected.

3At least one boy being selected.

4Exactly two girls and a boy being selected.

9One box contains three coins. Coin 1 is standard, Coin 2 has two heads and Coin 3 is rigged so that the probability of getting heads is 1/3. A coin is randomly selected from the box and thrown into the air. Find the probability of obtaining a result of heads.

## 1

If A and B are two random events with probabilities of p(A) = 1/2, p(B) = 1/3, p(A B)= 1/4, calculate:

1

2

3

4

5

## 2

If A and B are two random events with probabilities of p(A) = 1/3, p(B) = 1/4, p(A B) = 1/5, calculate:

1

2

3

4

5

6

## 3

Students in a high school can choose to study Spanish or French as a foreign language. In a given academic year, 90% of the pupils choose Spanish and the rest choose French. 30% of the students who are learning Spanish are boys and 40% who are studying French are also boys. If a student was randomly selected from this academic year, what is the probability that it would be a girl?

p(girl) = 0.9 · 0.7 + 0.1 · 0.6 = 0.69

## 4

Two cards are removed simultaneously from a deck of 48 cards. Calculate the probability of drawing:

1 Two diamonds.

2At least one diamond.

3One diamond and one heart.

## 5

A student has studied only 15 of the 25 topics covered in a semester for a particular class. For the exam, the student is allowed to randomly select two issues and choose one of the two to write about. Find the probability that the student will choose one of the topics that he has studied.

## 6

A class is formed by 10 boys and 10 girls. Half of the girls and half of the boys have selected French as their optional subject.

1 What is the probability that a randomly selected student is a boy or somebody who studies French?

2What is the probability that a randomly selected student is girl who does not study French?

## 7

A car workshop knows that on an average morning: three cars with electrical problems, eight with mechanical problems and three with sheet metal problems arrive at the shop for service. In the afternoon, two cars with electrical problems, three with mechanical problems and one car with sheet problems also arrive at the shop.

1 Create a table ordering the data.

2Calculate the percentages of the cars who arrive in the afternoon.

3Calculate the percentage of the cars that arrive with mechanical problems.

4Calculate the probability that a car with electrical problems will arrive in the morning.

## 8

A class consists of six girls and ten boys. If a committee of three is chosen at random, find the probability of:

1 Three boys being selected.

2Exactly two boys and a girl being selected.

3At least one boy being selected.

4Exactly two girls and a boy being selected.

## 9

One box contains three coins. Coin 1 is standard, Coin 2 has two heads and Coin 3 is rigged so that the probability of getting heads is 1/3. A coin is randomly selected from the box and thrown into the air. Find the probability of obtaining a result of heads.