$A$ and $B$ are events such that $\mathrm{P}(A' \cap B') = \frac{1}{7}$, \(\mathrm{P}(A \

Question

$A$ and $B$ are events such that $\mathrm{P}(A' \cap B') = \frac{1}{7}$, $\mathrm{P}(A \cap B') = \frac{2}{5}$ and $\mathrm{P}(A | B) = \frac{5}{8}$. Find $\mathrm{P}(A \cap B)$.[3] Explain whether the events $A$ and $B$ are independent.[3] Explain the meaning of $\mathrm{P}(A' \cup B')$.[1]

Accepted Answer

(a) $\frac27$. (b) Not independent: $\mathrm{P}(A\mid B)\ne\mathrm{P}(A)$. (c) The probability that at least one of $A$ and $B$ fails to occur; $\frac57$.

2024 YIJC H1 Q8

2024 YIJC H1 Q8

Solution:

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