# Lesson Worksheet: Mutually Exclusive Events Mathematics

In this worksheet, we will practice identifying mutually exclusive events and finding their probabilities.

Q1:

A bag contains 41 balls. There are 28 red balls which are numbered 1 to 28 and 13 white balls which are numbered 29 to 41. If a ball is chosen from the bag at random, what is the probability of the ball being red and having an even number?

• A
• B
• C
• D
• E

Q2:

Suppose that and are two mutually exclusive events. The probability of the event occurring is five times that of the event occurring. Given that the probability that one of the two events occurs is 0.18, find the probability of event occurring.

Q3:

A bag contains fifty-one balls numbered 1 to 51. If one ball is randomly drawn from the bag without looking, what is the probability that is is numbered 17 or 27? Give your answer as a fraction in its simplest form.

• A
• B
• C
• D
• E

Q4:

A bag contains red, blue, and green balls, and one is to be selected without looking. The probability that the chosen ball is red is equal to seven times times the probability that the chosen ball is blue. The probability that the chosen ball is blue is the same as the probability that the chosen ball is green.

Find the probability that the chosen ball is red or green.

• A
• B
• C
• D

Q5:

A deck of cards numbered from 1 to 35 is shuffled and a card is chosen. What is the probability that the chosen card has a number that is divisible by 8 and 6?

• A
• B
• C
• D
• E

Q6:

A survey asked 49 people if they had visited any clubs recently. 28 had attended club , 38 had attended club , and 8 had not been to either club. What is the probability that a random person from the sample attended both clubs?

• A
• B
• C
• D

Q7:

The probability that a student passes their physics exam is 0.71. The probability that they pass their mathematics exam is 0.81. The probability that they pass both exams is 0.68. What is the probability that the student only passes their mathematics exam?

Q8:

A small choir has a tenor singer, 3 soprano singers, a baritone singer, and a mezzo-soprano singer. If one of their names was randomly chosen, determine the probability that it was the name of the tenor singer or soprano singer.

• A
• B
• C
• D

Q9:

In an experiment a coin is flipped and a die rolled once, then the upper face of each is observed. is the event that the coin lands head side up and the die lands showing a prime number. is the event that the die lands showing an even number. Find the probability of the occurrence of the two events and together.

• A
• B
• C
• D
• E

Q10:

A card is picked at random from a standard deck of cards. Let be the event that a king is picked and let be the event that a red card is picked.

Find , giving your answer as a fraction in its simplest form.

• A
• B
• C
• D
• E

Find , giving your answer as a fraction in its simplest form.

• A
• B
• C
• D
• E

Find , giving your answer as a fraction in its simplest form.

• A
• B
• C
• D
• E

Find , giving your answer as a fraction in its simplest form.

• A
• B
• C
• D
• E

Q11:

Amelia has a deck of 52 cards. She randomly selects one card and considers the following events:

Event A: picking a card that is a heart;

Event B: picking a card that is black

Event C: picking a card that is not a spade

Are events A and B mutually exclusive?

• ANo
• BYes

Are events A and C mutually exclusive?

• ANo
• BYes

Are events B and C mutually exclusive?

• AYes
• BNo

Q12:

Amelia has these 10 cards. Choose a Venn diagram for the experiment of randomly picking a card that shows the two events “picking a multiple of 3” and “picking a square number.”

• A • B • C • D • E Are the events “picking a multiple of 3” and “picking a square number” mutually exclusive?

• ANo
• BYes

What is the probability of picking a number that is a multiple of 3 and a square number? Give your answer as a fraction in its simplest form.

• A3/5
• B2/5
• C9/10
• D1/10
• E1/5

Q13:

A random experiment has sample space . Given that and , find .

• A
• B
• C
• D

Q14:

A random experiment has sample space . Given and , find .

• A
• B
• C
• D

Q15:

A bag contains balls labeled 10, 11, or 12. In an experiment, a ball is selected at random, and the probability of each outcome is shown in the table. Find the value of .

 Number Probability 10 11 12 𝑥 0.5 0.4

Q16:

Which of the following is true if ?

• AEvents and are independent.
• BEvents and have equal probabilities.
• CEvents and are collectively exhaustive.
• DThe probability of the intersection of events and is equal to the probability of their union.
• EEvents and are mutually exclusive.

Q17:

Given that and are two mutually exclusive events in a sample space of a random experiment, determine .

• A
• B
• C
• D

Q18:

Two mutually exclusive events and have probabilities and . Find .

• A
• B
• C
• D

Q19:

If a die is rolled once, then what is the probability of getting an odd and an even number together?

Q20:

Suppose and are mutually exclusive events. Determine .

Q21:

Suppose , , and are three mutually exclusive events in a sample space . Given that , , and , find .

• A
• B
• C
• D
• E

Q22:

Denote by and two mutually exclusive events. Given that and , determine .

Q23:

Suppose and are two mutually exclusive events. Given that and , find .

Q24:

If I roll a regular six-sided die, what is the probability that the score is an odd, prime number?

• A
• B
• C
• D

Q25:

What is the probability of rolling an even prime number on a fair die?

• A
• B
• C0
• D