Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4, she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what

Explanation

`E_{1}: = 1,2,3` or 4 is appear on die


`{E}_{2}:= 5` or `6` is appear on die


`E` := exactly one head appears


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therefore P(E_{1})=frac{4}{6}=frac{2}{3} text { and } P(E_{2})=frac{2}{6}=frac{1}{3}
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`P(E | E_{1})=P(` head apperars when coin is tossed one time )`=frac{1}{2}`


and `P(E | E_{2})=P` (exactly one head appears when coin is tossed thrice )


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