Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin 3 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 is the probability that she threw 1,2,3, or 4 with the die? site:shaalaa.com

Explanation

`E_{1}, E_{2}`, `E` is events


`E_{1}: ' 1,2,3` or 4 is shown on die


`E_{2}: ' 5` or 6 is shown on die


`E` : 'exactly one head shows up


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therefore quad 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 shows when coin is toss one time )`=frac{1}{2}`


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