Lesson Worksheet: Operations on Events Mathematics • 10th Grade

In this worksheet, we will practice finding the probabilities of the complement, intersection, and union of events.

Q1:

Given that 𝐴 and 𝐵 are two events in the sample space of a random experiment, where 𝐴𝐵, determine 𝐴𝐵.

  • A𝐵
  • B𝐴𝐵
  • C𝐴
  • D

Q2:

Suppose 𝐴 and 𝐵 are events such that 𝐵𝐴. Determine 𝐴𝐵.

  • A𝐵
  • B𝐴𝐵
  • C𝐴
  • D

Q3:

Denote by 𝐴 and 𝐵 two events with probabilities 𝑃(𝐴)=0.2 and 𝑃(𝐵)=0.47. Given that 𝑃(𝐴𝐵)=0.18, find 𝑃(𝐴𝐵).

Q4:

Denote by 𝐴 and 𝐵 two events with probabilities 𝑃(𝐴)=0.58 and 𝑃(𝐵)=0.2. Given that 𝑃(𝐴𝐵)=0.64, find 𝑃(𝐴𝐵).

Q5:

Suppose 𝐴 and 𝐵 are two events with probability 𝑃(𝐴)=0.6 and 𝑃(𝐵)=0.5. Given that 𝑃(𝐴𝐵)=0.4, what is the probability that neither of the events occur?

Q6:

A group of 68 school children completed a survey asking about their television preferences. The results show that 43 of the children watch channel 𝐴, 26 watch channel 𝐵, and 12 watch both channels. If a child is selected at random from the group, what is the probability that they watch at least one of the two channels?

  • A4368
  • B734
  • C1334
  • D3168
  • E5768

Q7:

𝐴 and 𝐵 are two events in a sample space of a random experiment and 𝑃(𝐴)=79𝑃(𝐵). The probability that at most one of 𝐴 or 𝐵 occurs is 0.56. The probability that at least one of 𝐴 or 𝐵 occurs is 0.68. Find the probability that 𝐴 occurs OR 𝐵 does not occur.

Q8:

Suppose that 𝑋 and 𝑌 are two events with probabilities 𝑃(𝑌)=13 and 𝑃(𝑋)=𝑃𝑋. Given that 𝑃(𝑋𝑌)=18, determine 𝑃(𝑋𝑌).

  • A724
  • B524
  • C1332
  • D1724
  • E56

Q9:

Suppose 𝐴 and 𝐵 are events. Given that 𝑃(𝐴)=4𝑥, 𝑃𝐵=𝑥,𝑃(𝐴𝐵)=3𝑥+0.9, and 𝑃(𝐴𝐵)=12𝑥, find the value of 𝑥.

  • A35
  • B14
  • C15
  • D519

Q10:

Suppose 𝐴 and 𝐵 are events in a sample space which consists of equally likely outcomes. Given that the number of outcomes in 𝐴 is 3, the number of outcomes in 𝐵 is 11, the number of outcomes common to both 𝐴 and 𝐵 is 2, and 𝑃(𝐴𝐵)=38, find 𝑃𝐴𝐵.

  • A38
  • B332
  • C3132
  • D1516
  • E1132

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