Lesson Worksheet: Operations on Events: Difference Mathematics

In this worksheet, we will practice finding the probability of the difference of two events.

Q1:

Suppose 𝐴 and 𝐵 are two events with probabilities 𝑃(𝐴)=57 and 𝑃(𝐵)=47. Given that 𝑃(𝐴𝐵)=67, determine 𝑃(𝐴𝐵).

  • A715
  • B37
  • C57
  • D27
  • E79

Q2:

Suppose 𝐴 and 𝐵 are two events. Given that 𝐵𝐴, 𝑃(𝐵)=49, and 𝑃(𝐴𝐵)=15, determine 𝑃(𝐴).

  • A245
  • B2845
  • C2945
  • D845
  • E619

Q3:

A ball is drawn at random from a bag containing 12 balls each with a unique number from 1 to 12. Suppose 𝐴 is the event of drawing an odd number and 𝐵 is the event of drawing a prime number. Find 𝑃(𝐴𝐵).

  • A112
  • B512
  • C13
  • D16
  • E12

Q4:

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

  • A𝐵
  • B
  • C𝐴
  • D𝐴𝐵

Q5:

𝐴 and 𝐵 are two events in a sample space of a random experiment where 𝑃(𝐴)=310, 𝑃(𝐵)=15, and 𝑃(𝐴𝐵)=110. Find 𝑃(𝐴𝐵).

  • A35
  • B15
  • C310
  • D110

Q6:

Suppose 𝐴 and 𝐵 are two events. Given that 𝑃(𝐴)=58, 𝑃(𝐵)=34, and 𝑃(𝐴𝐵)=14, find 𝑃𝐴𝐵.

  • A34
  • B54
  • C58
  • D18
  • E12

Q7:

Suppose 𝐴 and 𝐵 are two events in a random experiment. Given that 𝑃(𝐵)=710𝑃(𝐴), 𝑃(𝐴𝐵)=0.12, and 𝑃𝐵𝐴=0.03, find 𝑃(𝐵).

Q8:

Suppose 𝐴 and 𝐵 are events in a sample space 𝑆. Given that 𝑃(𝐴)=𝑃(𝐵), 𝑃(𝐴𝐵)=0.72, and 𝑃(𝐴𝐵)=0.76, find 𝑃(𝑆𝐵).

Q9:

Suppose 𝐴 and 𝐵 are two events. Given that 𝑃𝐴=57𝑃(𝐴𝐵)=0.44 and 𝑃(𝐴𝐵)=0.33, find 𝑃(𝐵).

Q10:

Suppose that 𝐴 and 𝐵 are events in a random experiment. Given that 𝑃(𝐴)=0.71, 𝑃(𝐵)=0.47, and 𝑃(𝐴𝐵)=0.99, determine 𝑃(𝐵𝐴).

This lesson includes 24 additional questions and 259 additional question variations for subscribers.

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