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Lesson Worksheet: Mutually Exclusive Events Mathematics

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

Q1:

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

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

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

  • ANot mutually exclusive
  • BMutually exclusive

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

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

  • AMutually exclusive
  • BNot mutually exclusive

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

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

  • AMutually exclusive
  • BNot mutually exclusive

Q2:

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

Q3:

If 𝐴 and 𝐡 are two mutually exclusive events from a sample space of a random experiment, find 𝑃𝐴βˆͺ𝐡.

Q4:

Suppose 𝐴 and 𝐡 are two mutually exclusive events. Given that 𝑃(π΄βˆ’π΅)=0.52, find 𝑃(𝐴).

Q5:

Two mutually exclusive events 𝐴 and 𝐡 have probabilities 𝑃(𝐴)=110 and 𝑃(𝐡)=15. Find 𝑃(𝐴βˆͺ𝐡).

  • A310
  • B910
  • C110
  • D45

Q6:

Suppose 𝐴 and 𝐡 are two mutually exclusive events. Given that 𝑃(𝐴βˆͺ𝐡)=0.93 and 𝑃(π΄βˆ’π΅)=0.39, find 𝑃(𝐡).

Q7:

Suppose 𝐴 and 𝐡 are two mutually exclusive events. Given that 𝑃𝐴=0.61 and 𝑃(𝐴βˆͺ𝐡)=0.76, determine 𝑃(𝐡).

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 theΒ tenor singer or soprano singer.

  • A12
  • B16
  • C23
  • D13

Q9:

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.

  • A815
  • B89
  • C19
  • D29

Q10:

In an animal rescue shelter, 39%β€Ž of the current inhabitants are cats (C) and 41%β€Ž are dogs (D).

Find the probability that an animal chosen at random is either a cat or a dog.

Find the probability that an animal chosen at random is neither a cat nor a dog.

This lesson includes 23 additional questions and 164 additional question variations for subscribers.

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