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 probabilities of members A, B, and C not attending are $P(A') = 0.10$, $P(B') = 0.20$, and $P(C') = 0.05$, respectively. The meeting is cancelled if at least one member is absent, which is given by $P(\text{cancelled}) = P(A' \cup B' \cup C')$. This can be calculated as $1 - P(A \cap B \cap C)$, where $P(A \cap B \cap C)$ is the probability that all three members attend. Assuming independence, $P(A \cap B \cap C) = P(A) \cdot P(B) \cdot P(C) = (1 - P(A')) \cdot (1 - P(B')) \cdot (1 - P(C')) = (1 - 0.10) \cdot (1 - 0.20) \cdot (1 - 0.05) = 0.90 \cdot 0.80 \cdot 0.95 = 0.684$. Therefore, the probability of the meeting being cancelled is $P(\text{cancelled}) = 1 - 0.684 = 0.316$.