# Lesson Worksheet: Mutually Exclusive and Exhaustive Events Mathematics

In this worksheet, we will practice recognizing and working with mutually exclusive outcomes and determining when events are exhaustive.

**Q1: **

Mariam 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?

- AYes
- BNo

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

**Q2: **

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

**Q3: **

A fair coin is flipped and a fair die is rolled. What is the probability of rolling an even number on the die?

- A
- B
- C
- D

**Q4: **

In each case, decide whether the two events are mutually exclusive or not.

Event : Rolling a 6-sided die and getting a number greater than 4.

Event : Rolling a 6-sided die and getting an odd number.

- ANot mutually exclusive
- BMutually exclusive

Event : Rolling an 8-sided die and getting a number less than 4.

Event : Rolling an 8-sided die and getting a number greater than 4.

- AMutually exclusive
- BNot mutually exclusive

Event : Rolling a 20-sided die and getting a prime number greater than 3.

Event : Rolling a 20-sided die and getting a factor of 15.

- AMutually exclusive
- BNot mutually exclusive

**Q5: **

A bag contains a number of balls that are identical except for their colors. The probabilities of choosing a green, a blue, and a red ball at random are , , and respectively.

Are there balls of other colors in the bag?

- AYes
- BNo

If is the event of choosing a green ball from the bag and is the event of choosing a blue one, are and mutually exclusive?

- AYes
- BNo

What is the probability of choosing a green or a blue ball?

- A
- B
- C
- D
- ENone of the above

**Q6: **

The table shows the grades of 25 students in a class.

A | B | C | D | F | |
---|---|---|---|---|---|

Male | 1 | 3 | 2 | 3 | 2 |

Female | 5 | 4 | 2 | 2 | 1 |

Find the probability of choosing a student with grade A.

Find the probability of choosing a female student with grade B.

Consider the following events:

- : The student is male.
- : The student is female.
- : The student got a grade A.
- : The student got a grade B.

Which of the following pairs are mutually exclusive?

- A and
- B and
- C and
- D and
- E and

**Q7: **

A student is taking two courses, mathematics and science. The probability that the student will pass the mathematics course is 0.27.

What is the probability that the student will **not** pass the mathematics course?

What is the probability that the student will pass the science course?

- A0.73
- B0.5
- C0.27
- D0.135
- EThere is not enough information provided to answer this question.

If the probability that the student will pass the science course is 0.73, are the events (passing the science course and passing the mathematics course) mutually exclusive?

- ANo
- BYes
- CThere is not enough information provided to answer this question.

**Q8: **

Fill in the blank: If the probability of getting a head when tossing a biased coin is , then the probability of getting a tail is .

- A
- B
- C
- D
- E

**Q9: **

Fill in the blank: If a set of pairwise mutually exclusive events are also exhaustive, then their probabilities sum to .

**Q10: **

A fair die is rolled. Consider that event is getting a prime number and event is getting an even number.

Find the sample spaces of events and .

- A
- B
- C
- D
- E

Find and .

- A,
- B,
- C,
- D,
- E,

Are events and mutually exclusive?

- AYes
- BNo

Let be the event of getting 1, 4, or 6 on the upper face of the die. Which of the following is true?

- A and are exhaustive events.
- B and are mutually exclusive.
- C and are not mutually exclusive.
- D and are mutually exclusive and .
- E and are mutually exclusive and .