Let $A$ and $B$ be events such that $\mathrm{P}\left( A'\cap B \right)=0.13$, \(\mat

Question

Let $A$ and $B$ be events such that $\mathrm{P}\left( A'\cap B \right)=0.13$, $\mathrm{P}\left( A'\cap B' \right)=0.38$ and $\mathrm{P}\left( A|B \right)=0.675$. Find $\mathrm{P}\left( A\cap B \right)$.[3] Determine whether $A$ and $B$ are independent.[1] Two players, $C$ and $D$, compete in a match. The probability that $C$ wins the first set is $p$. For each set after the first, the conditional probability that any player wins the set, given that the player won the preceding set, is $p$. Each set is won either by player $C$ or $D$. If there is no limit to the number of sets played, and a match is won only when a player wins two consecutive sets, show that the probability that $C$ wins the match is $\frac{1-p+{{p}^{2}}}{2-p}$.[3]

Accepted Answer

(a)(i) $0.27$ (ii) $A$ and $B$ are not independent (b) $\frac{1-p+p^2}{2-p}$

2015 HCI P2 Q6

2015 HCI P2 Q6

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