April 19, 2021

Chapters

## Exercise 1

In a class in which all students practice at least one sport, 60% of students play soccer or basketball and 10% practice both sports. If there is also 60% that do not play soccer, calculate the probability that a student chosen at random from the class:

1 Plays soccer only.

2 Plays basketball only.

3 Plays only one of the sports.

4 Plays neither soccer nor basketball.

## Exercise 2

In a city, 40% of the population have brown hair, 25% have brown eyes and 15% have both brown hair and eyes. A person is chosen at random.

1 If they have brown hair, what is the probability that they also have brown eyes?

2 If they have brown eyes, what is the probability of them not having brown hair?

3 What is the probability of them having neither brown hair nor brown eyes?

## Exercise 3

There are two boxes. Box A contains 6 red balls and 4 blue balls and Box B contains 4 red balls and 8 blue balls. A die is rolled, if the number is less than 3, a ball is selected from box A. If the result is 3 or more, a ball is selected from Box B. Calculate:

1 The probability that the ball will be red and selected from Box B.

2 The probability that the ball will be blue.

## Exercise 4

In order to write an exam, a student needs an alarm clock to wake up, which has proven to successfully wake him 80% of the time. If he hears the alarm in the morning the probability of writing the test is 0.9 and if he doesn´t hear the alarm the probability is 0.5.

1 If he writes the test what is the probability that he heard the alarm clock?

2 If he doesn´t write the test: what is the probability that he didn´t hear the alarm clock?

## Exercise 5

On a shelf there are 60 novels and 20 poetry books. Person A chooses a book at random off the shelf and leaves with it. Shortly after, Person B chooses another book at random. Calculate:

1 The probability that the book selected by Person B is a novel?

2 If it is known that Person B chose a novel: what is the probability that the book selected by Person A was a poetry book?

## Exercise 6

It is determined that 25 of every 100 men and 600 of every 1,000 women wear glasses. If the number of women in a particular room is four times more than that of men, calculate the probability of:

1 A person without glasses being randomly selected.

2 A woman with glasses being randomly selected.

## Exercise 7

There are three sets of key rings A, B and C, for a house. The first set has five keys, the second has seven and the third has eight, of which only one key in each set opens the door to the store room. A keychain is chose at random followed by a key from the set.

1 What is the probability of the selected key being able to open the store room?

2 What is the probability that the chosen key chain is from the third set and the key does not open the door?

3 What is the probability that the chosen key opens the door and it came from the first key chain?

## Solution of exercise 1

In a class in which all students practice at least one sport, 60% of students play soccer or basketball and 10% practice both sports. If there are 60% students who do not play soccer, calculate the probability that a student chosen at random from the class:

1 Plays soccer only.

2 Plays basketball only.

3 Plays only one of the sports

4 Plays neither soccer nor basketball

## Solution of exercise 2

In a city, 40% of the population have brown hair, 25% have brown eyes and 15% have both brown hair and eyes. A person is chosen at random.

1 If they have brown hair, what is the probability that they also have brown eyes?

p (Brown eyes | Brown hair) =

2 If they have brown eyes, what is the probability of them not having brown hair?

p (No brown hair | Brown eyes) =

3 What is the probability of them having neither brown hair nor brown eyes?

p (neither brown hair or eyes) =

## Solution of exercise 3

There are two boxes. Box A contains 6 red balls and 4 blue balls and Box B contains 4 red balls and 8 blue balls. A die is rolled, if the number is less than 3, a ball is selected from box A. If the result is 3 or more, a ball is selected from Box B. Calculate:

1 The probability that the ball will be red and selected from Box B.

2 The probability that the ball will be blue.

p (Blue ball) =

## Solution of exercise 4

In order to write an exam, a student needs an alarm clock to wake up, which has proven to successfully wake him 80% of the time. If he hears the alarm in the morning the probability of writing the test is 0.9 and if he doesn´t hear the alarm the probability is 0.5.

1 If he writes the test what is the probability that he heard the alarm clock?

p (Heard |Test) =

2 If he doesn´t write the test: what is the probability that he didn´t hear the alarm clock?

p (No heard|No test) =

## Solution of exercise 5

On a shelf there are 60 novels and 20 poetry books. Person A chooses a book at random off the shelf and leaves with it. Shortly after, Person B chooses another book at random. Calculate:

1 The probability that the book selected by Person B is a novel?

p (B novel) =

2 If it is known that Person B chose a novel: what is the probability that the book selected by Person A was a poetry book?

p (A poetry | B novel) =

## Solution of exercise 6

It is determined that 25 of every 100 men and 600 of every 1,000 women wear glasses. If the number of women in a particular room is four times more than that of men, calculate the probability of:

1 A person without glasses being randomly selected.

p (No glasses) =

2 A woman with glasses being randomly selected.

p (Woman with glasses) =

## Solution of exercise 7

There are three sets of key rings A, B and C, for a house. The first set has five keys, the second has seven and the third has eight, of which only one key in each set opens the door to the store room. A keychain is chose at random followed by a key from the set.

1 What is the probability of the selected key being able to open the store room?

p (Open) =

2 What is the probability that the chosen key chain is from the third set and the key does not open the door?

p (C and not open) =

3 What is the probability that the chosen key opens the door and it came from the first key chain?

p (A|open) =