Meera visits only one of the two temples A an | vedclass

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Question

(D) Let $A$ be the event that Meera visits temple $A$ and $B$ be the event that she visits temple $B$. Let $F$ be the event that she meets her friend.

Vedclass · Accepted Answer

$\frac{9}{16}$

Vedclass · Answer

(D) Let $A$ be the event that Meera visits temple $A$ and $B$ be the event that she visits temple $B$. Let $F$ be the event that she meets her friend. Given: $P(A) = \frac{2}{5}$ $P(B) = 1 - P(A) = 1 - \frac{2}{5} = \frac{3}{5}$ $P(F|A) = \frac{1}{3}$ $P(F|B) = \frac{2}{7}$ We need to find the probability that she met her friend at temple $B$,which is $P(B|F)$. Using Bayes' Theorem: $P(B|F) = \frac{P(B) 	imes P(F|B)}{P(A) 	imes P(F|A) + P(B) 	imes P(F|B)}$ $P(B|F) = \frac{\frac{3}{5} 	imes \frac{2}{7}}{(\frac{2}{5} 	imes \frac{1}{3}) + (\frac{3}{5} 	imes \frac{2}{7})}$ $P(B|F) = \frac{\frac{6}{35}}{\frac{2}{15} + \frac{6}{35}}$ Finding a common denominator for the denominator: $15 = 3 	imes 5$ and $35 = 7 	imes 5$,so $LCM$ is $105$. $P(B|F) = \frac{\frac{6}{35}}{\frac{14}{105} + \frac{18}{105}} = \frac{\frac{18}{105}}{\frac{14+18}{105}} = \frac{18}{32} = \frac{9}{16}$

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