Question

A meeting will be held only if all three members A, B and C are present. The probability that member A does not turn up is 0.10, member B does not turn up is 0.20 and member C does not turn up is 0.05. The probability of the meeting being cancelled is:

• A. 0.35
• B. 0.316
• C. 0.001
• D. 0.65

Hint:

The probability of an event occurring is 1 minus the probability of its complement. For independent events, multiply their individual probabilities.

Answer 1

The Correct Option is B

The probability that member A does not turn up is $P(A') = 0.10$, member B does not turn up is $P(B') = 0.20$, and member C does not turn up is $P(C') = 0.05$. The probability that the meeting is cancelled is the probability that at least one of the members does not turn up: \[ P(\text{cancelled}) = P(A' \cup B' \cup C') = 1 - P(A \cap B \cap C) \] The probability that all three members turn up is: \[ P(A \cap B \cap C) = (1 - P(A')) \cdot (1 - P(B')) \cdot (1 - P(C')) = (1 - 0.10) \cdot (1 - 0.20) \cdot (1 - 0.05) = 0.90 \cdot 0.80 \cdot 0.95 = 0.684 \] Thus, the probability that the meeting is cancelled is: \[ P(\text{cancelled}) = 1 - 0.684 = 0.316 \]