On every evening,a student either watches TV | vedclass

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Question

(B) Let $T$ be the event that the student watches $TV$ and $B$ be the event that the student reads a book. Let $S$ be the event that the student falls

Vedclass · Accepted Answer

$\frac{12}{13}$

Vedclass · Answer

(B) Let $T$ be the event that the student watches $TV$ and $B$ be the event that the student reads a book. Let $S$ be the event that the student falls asleep.Given probabilities are:$P(T) = \frac{4}{5}$$P(B) = 1 - P(T) = 1 - \frac{4}{5} = \frac{1}{5}$$P(S|T) = \frac{3}{4}$$P(S|B) = \frac{1}{4}$We need to find $P(T|S)$,the probability that he watched $TV$ given that he is asleep.Using Bayes' Theorem:$P(T|S) = \frac{P(T) 	imes P(S|T)}{P(T) 	imes P(S|T) + P(B) 	imes P(S|B)}$$P(T|S) = \frac{(\frac{4}{5}) 	imes (\frac{3}{4})}{(\frac{4}{5}) 	imes (\frac{3}{4}) + (\frac{1}{5}) 	imes (\frac{1}{4})}$$P(T|S) = \frac{\frac{12}{20}}{\frac{12}{20} + \frac{1}{20}}$$P(T|S) = \frac{\frac{12}{20}}{\frac{13}{20}} = \frac{12}{13}$

Box	Black	White	Red	Blue
$I$	$3$	$4$	$5$	$6$
$II$	$2$	$2$	$2$	$2$
$III$	$1$	$2$	$3$	$1$
$IV$	$4$	$3$	$1$	$5$

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