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Worksheet: Probability of Mutually and Nonmutually Exclusive Events

Q1:

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

Q2:

A bag contains fifty-one balls numbered 1 to 76. If one ball is randomly drawn from the bag without looking, what is the probability that is is numbered 57 or 66? Give your answer as a fraction in its simplest form.

  • A 1 7 5
  • B 1 7 6
  • C 2 7 5
  • D 1 3 8
  • E 2 7 7

Q3:

A bag contains fifty-one balls numbered 1 to 61. If one ball is randomly drawn from the bag without looking, what is the probability that is is numbered 58 or 59? Give your answer as a fraction in its simplest form.

  • A 1 6 0
  • B 1 6 1
  • C 1 3 0
  • D 2 6 1
  • E 1 3 1

Q4:

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

Q5:

A bag contains 44 balls. There are 10 red balls which are numbered 1 to 10 and 34 white balls which are numbered 11 to 44. If a ball is chosen from the bag at random, what is the probability of the ball being white and having an odd number?

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

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:

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

Q8:

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

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

Q9:

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?

Q10:

The probability that a student passes their physics exam is 0.54. The probability that they pass their mathematics exam is 0.86. The probability that they pass both exams is 0.51. What is the probability that the student only passes their mathematics exam?

Q11:

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

Q12:

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?

  • AYes
  • BNo

Are events A and C mutually exclusive?

  • ANo
  • BYes

Are events B and C mutually exclusive?

  • AYes
  • BNo

Q13:

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

Q14:

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 ) .

Q15:

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

Q16:

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

Q17:

If and are two mutually exclusive events from a sample space of a random experiment, find .

Q18:

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

Q19:

A deck of cards numbered 1 to 67 is shuffled and a card is chosen. What is the probability that the chosen card has a number which is divisible by 2 and 5?

  • A 3 3 6 7
  • B 4 0 6 7
  • C 1 3 6 7
  • D 6 6 7
  • E 7 6 7

Q20:

A deck of cards numbered 1 to 55 is shuffled and a card is chosen. What is the probability that the chosen card has a number which is divisible by 4 and 5?

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

Q21:

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

Q22:

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

Q23:

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

Q24:

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.

Q25:

Suppose that 𝐴 and 𝐡 are two mutually exclusive events. The probability of the event 𝐡 occurring is four times that of the event 𝐴 occurring. Given that the probability that one of the two events occurs is 0.6, find the probability of event 𝐴 occurring.