Lesson Worksheet: Mutually Exclusive Events Mathematics • 10th Grade

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

Q1:

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

Event ๐ด: picking a card that is a heart;

Event ๐ต: picking a card that is black

Event ๐ถ: picking a card that is not a spade

Are events ๐ด and ๐ต mutually exclusive?

  • ANo
  • BYes

Are events ๐ด and ๐ถ mutually exclusive?

  • ANo
  • BYes

Are events ๐ต and ๐ถ mutually exclusive?

  • AYes
  • BNo

Q2:

Amelia has these 10 cards.

Choose a Venn diagram for the experiment of randomly picking a card that shows the two events โ€œpicking a multiple of 3โ€ and โ€œpicking a square number.โ€

  • A
  • B
  • C
  • D
  • E

Are the events โ€œpicking a multiple of 3โ€ and โ€œpicking a square numberโ€ 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

Q3:

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?

Q4:

Two mutually exclusive events ๐ด and ๐ต have probabilities ๐‘ƒ(๐ด)=110 and ๐‘ƒ(๐ต)=15. Find ๐‘ƒ(๐ดโˆช๐ต).

  • A310
  • B910
  • C110
  • D45

Q5:

Suppose ๐ด and ๐ต are two mutually exclusive events. Given that ๐‘ƒ(๐ต)=4๐‘ƒ(๐ด) and ๐‘ƒ(๐ดโˆช๐ต)=0.95, find ๐‘ƒ(๐ต).

Q6:

A survey asked 49 people if they had visited any clubs recently. 28 had attended club ๐ด, 38 had attended club ๐ต, and 8 had not been to either club. What is the probability that a random person from the sample attended both clubs?

  • A47
  • B849
  • C2549
  • D4149

Q7:

Suppose ๐ด, ๐ต, and ๐ถ are three mutually exclusive events in a sample space ๐‘†. Given that ๐‘†=๐ดโˆช๐ตโˆช๐ถ, ๐‘ƒ(๐ด)=15๐‘ƒ(๐ต), and ๐‘ƒ(๐ถ)=4๐‘ƒ(๐ด), find ๐‘ƒ(๐ตโˆช๐ถ).

  • A25
  • B13
  • C12
  • D15
  • E910

Q8:

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 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.

  • A815
  • B89
  • C19
  • D29

Q9:

Suppose that ๐ด and ๐ต are two mutually exclusive events. The probability of the event ๐ต occurring is five times that of the event ๐ด occurring. Given that the probability that one of the two events occurs is 0.18, find the probability of event ๐ด occurring.

Q10:

Which of the following is true if ๐‘ƒ(๐ดโˆช๐ต)=๐‘ƒ(๐ด)+๐‘ƒ(๐ต)?

  • AEvents ๐ด and ๐ต are independent.
  • BEvents ๐ด and ๐ต have equal probabilities.
  • CEvents ๐ด and ๐ต are collectively exhaustive.
  • DThe probability of the intersection of events ๐ด and ๐ต is equal to the probability of their union.
  • EEvents ๐ด and ๐ต are mutually exclusive.

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