Given that the two events $A$ and $B$ are such that \(\mathrm{P}(A|B)=\frac{2}{3},\,\,\math

Question

Given that the two events $A$ and $B$ are such that $\mathrm{P}(A|B)=\frac{2}{3},\,\,\mathrm{P}(A\cap B'\,)=\frac{1}{4}$ and $\mathrm{P}(A\cap B)=\frac{5}{12}$, determine if $A$ and $B$ are independent,[1] find $\mathrm{P}(A\cup B)$.[2] Ali and Bob take turns to shoot an arrow in an Archery training session. The probability that Ali hits the bull’s eye is $0.3$ and for Bob, it is $0.4$. Ali shoots first. Find the probability that Ali hits the bull’s eye first.[3] Calvin, his parents and $7$ other people are seated in a round table of $10$. Find the probability that his parents are seated together but Calvin is not seated beside either of his parents.[2]

Accepted Answer

(a) (i) Since ${P(A) = \frac{2}{3} = P(A\vert{}B)}$, therefore ${A}$ and ${B}$ are independent (ii) ${\frac{7}{8}}$ (b) ${\frac{15}{29}}$ (c) ${\frac{1}{6}}$

2012 SAJC P2 Q7

2012 SAJC P2 Q7

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