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 𝐡 are two events in the sample space of a random experiment, where π΄βŠ‚π΅, determine 𝐴∩𝐡.

  • A𝐡
  • B𝐴βˆͺ𝐡
  • C𝐴
  • Dβˆ…

Q2:

Suppose 𝐴 and 𝐡 are events such that π΅βŠ‚π΄. Determine 𝐴βˆͺ𝐡.

  • A𝐡
  • B𝐴∩𝐡
  • C𝐴
  • Dβˆ…

Q3:

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

Q4:

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

Q5:

Suppose 𝐴 and 𝐡 are two events with probability 𝑃(𝐴)=0.6 and 𝑃(𝐡)=0.5. Given that 𝑃(𝐴∩𝐡)=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 𝐡, 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 𝐡 are two events in a sample space of a random experiment and 𝑃(𝐴)=79𝑃(𝐡). The probability that at most one of 𝐴 or 𝐡 occurs is 0.56. The probability that at least one of 𝐴 or 𝐡 occurs is 0.68. Find the probability that 𝐴 occurs OR 𝐡 does not occur.

Q8:

Suppose that 𝑋 and π‘Œ are two events with probabilities 𝑃(π‘Œ)=13 and 𝑃(𝑋)=𝑃𝑋. Given that 𝑃(π‘‹βˆ©π‘Œ)=18, determine 𝑃(𝑋βˆͺπ‘Œ).

  • A724
  • B524
  • C1332
  • D1724
  • E56

Q9:

Suppose 𝐴 and 𝐡 are events. Given that 𝑃(𝐴)=4π‘₯, 𝑃𝐡=π‘₯,𝑃(𝐴βˆͺ𝐡)=3π‘₯+0.9, and 𝑃(𝐴∩𝐡)=12π‘₯, find the value of π‘₯.

  • A35
  • B14
  • C15
  • D519

Q10:

Suppose 𝐴 and 𝐡 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 𝐡 is 11, the number of outcomes common to both 𝐴 and 𝐡 is 2, and 𝑃(𝐴βˆͺ𝐡)=38, find 𝑃𝐴βˆͺ𝐡.

  • A38
  • B332
  • C3132
  • D1516
  • E1132

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