Worksheet: Probability of Mutually and Nonmutually Exclusive Events

In this worksheet, we will practice finding the probability of mutually and non-mutually exclusive events.

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 1 3 4 1
  • B 2 8 4 1
  • C 7 4 1
  • D 1 4 4 1
  • E 4 2 4 1

Q2:

Suppose that 𝐴 and 𝐡 are two mutually exclusive events. The probability of the event 𝐡 occurring is five times that of the event 𝐴 occurring. Given that the probability that one of the two events occurs is 0.18, find the probability of event 𝐴 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 1 5 0
  • B 1 5 1
  • C 1 2 5
  • D 2 5 1
  • E 1 2 6

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 8 1 5
  • B 1 9
  • C 2 9
  • D 8 9

Q5:

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

  • A 4 3 5
  • B 8 3 5
  • C 1 7
  • D 1 3 5
  • E 2 3 5

Q6:

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

  • A 4 7
  • B 8 4 9
  • C 4 1 4 9
  • D 2 5 4 9

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:

Suppose 𝐴 and 𝐡 are two mutually exclusive events. Given that 𝑃 ο€Ί 𝐴  = 0 . 6 1 and 𝑃 ( 𝐴 βˆͺ 𝐡 ) = 0 . 7 6 , determine 𝑃 ( 𝐡 ) .

Q9:

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 1 2
  • B 1 6
  • C 1 3
  • D 2 3

Q10:

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

  • A 1 4
  • B 1 6
  • C 1 3
  • D 1 1 2
  • E 1 8

Q11:

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

Find 𝑃 ( 𝐴 ) , giving your answer as a fraction in its simplest form.

  • A 1 5 2
  • B 1 4
  • C 3 1 3
  • D 1 1 3
  • E 1 2

Find 𝑃 ( 𝐡 ) , giving your answer as a fraction in its simplest form.

  • A 1 2
  • B 3 1 3
  • C 3 4
  • D 1 4
  • E 1 1 3

Find 𝑃 ( 𝐴 ∩ 𝐡 ) , giving your answer as a fraction in its simplest form.

  • A 1 1 2 6
  • B 1 5 2 6
  • C 1 2 6
  • D 1 1 3
  • E 1 2

Find 𝑃 ( 𝐴 βˆͺ 𝐡 ) , giving your answer as a fraction in its simplest form.

  • A 7 1 3
  • B 6 1 3
  • C 1 2 6
  • D 1 5 2 6
  • E 1 2

Q12:

Suppose 𝐴 and 𝐡 are two mutually exclusive events. Given that 𝑃 ( 𝐴 βˆ’ 𝐡 ) = 0 . 5 2 , find 𝑃 ( 𝐴 ) .

Q13:

Suppose 𝐴 and 𝐡 are two mutually exclusive events. Given that 𝑃 ( 𝐴 βˆͺ 𝐡 ) = 0 . 9 3 and 𝑃 ( 𝐴 βˆ’ 𝐡 ) = 0 . 3 9 , find 𝑃 ( 𝐡 ) .

Q14:

Suppose 𝐴 and 𝐡 are two mutually exclusive events. Given that 𝑃 ( 𝐡 ) = 7 9 and 𝑃 ( 𝐴 βˆ’ 𝐡 ) = 1 5 , determine 𝑃 ( 𝐴 ) .

  • A 7 9 0
  • B 4 4 4 5
  • C 4 3 9 0
  • D 1 5

Q15:

If 𝐴 and 𝐡 are two mutually exclusive events from a sample space of a random experiment, find 𝑃 ( 𝐴 βˆͺ 𝐡 ) β€² β€² .

Q16:

Given that 𝐴 and 𝐡 are two mutually exclusive events in the sample space of a random experiment, determine 𝐴 βˆ’ 𝐡 .

  • A βˆ…
  • B 𝐡
  • C 𝐡 βˆ’ 𝐴
  • D 𝐴

Q17:

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

  • A 𝐴 βˆ’ 𝐡
  • B βˆ…
  • C 𝐴
  • D 𝐡

Q18:

Dina 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?

  • AYes
  • BNo

Are events A and C mutually exclusive?

  • ANo
  • BYes

Are events B and C mutually exclusive?

  • AYes
  • BNo

Q19:

Amelia has these 10 cards.

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

  • A
  • B
  • C
  • D
  • E

Are the events β€œpicking a multiple of 3” and β€œpicking 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
  • B9/10
  • C1/10
  • D2/5
  • E1/5

Q20:

A random experiment has sample space { 𝐴 , 𝐡 , 𝐢 , 𝐷 } . Given that 𝑃 ( 𝐴 ) = 2 𝑃 ( 𝐡 ) and 𝑃 ( 𝐢 ) = 𝑃 ( 𝐷 ) = 1 5 , find 𝑃 ( 𝐴 ) .

  • A 4 1 5
  • B 1 5
  • C 8 1 5
  • D 2 5

Q21:

A random experiment has sample space { 𝐴 , 𝐡 , 𝐢 , 𝐷 } . Given 𝑃 ( 𝐴 ) = 2 𝑃 ( 𝐡 ) and 𝑃 ( 𝐢 ) = 𝑃 ( 𝐷 ) = 3 8 , find 𝑃 ( 𝐡 ) .

  • A 5 2 4
  • B 1 6
  • C 5 1 2
  • D 1 1 2

Q22:

A bag contains balls labelled 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 π‘₯ .

Number 10 11 12
Probability π‘₯ 0.5 0.4

Q23:

Which of the following is true if 𝑃 ( 𝐴 βˆͺ 𝐡 ) = 𝑃 ( 𝐴 ) + 𝑃 ( 𝐡 ) ?

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

Q24:

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

  • A 𝐡
  • B 𝐴
  • C 𝐴 βˆͺ 𝐡
  • D βˆ…

Q25:

Two mutually exclusive events 𝐴 and 𝐡 have probabilities 𝑃 ( 𝐴 ) = 1 1 0 and 𝑃 ( 𝐡 ) = 1 5 . Find 𝑃 ( 𝐴 βˆͺ 𝐡 ) .

  • A 9 1 0
  • B 1 1 0
  • C 4 5
  • D 3 1 0

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