Q.13   Probability that A speaks truth is \frac{4}{5} . A coin is tossed. A reports that a head appears. The probability that actually there was head is

               (A)  \frac{4}{5}

               (B)  \frac{1}{2}

                C)  \frac{1}{5}

               (D)  \frac{2}{5}

 

Answers (1)

Let   A : A speaks truth

        B : A  speaks false

P(A)=\frac{4}{5}

P(B)=1-\frac{4}{5}=\frac{1}{5}

X : Event that head appears.

A coin is tossed , outcomes are head or tail.

Probability of getting head whether A speaks thruth or not is \frac{1}{2}

P(X|A)=P(X|B)=\frac{1}{2}

P(A|X)= \frac{P(A).P(X|A)}{P(B).P(X|B)+P(A).P(X|A)}

P(A|X)= \frac{\frac{4}{5}\times \frac{1}{2}}{\frac{4}{5}\times \frac{1}{2}+\frac{1}{5}\times \frac{1}{2}}

P(A|X)= \frac{\frac{4}{5}}{\frac{4}{5}+\frac{1}{5}}

P(A|X)= \frac{\frac{4}{5}}{\frac{1}{1}}

P(A|X)={\frac{4}{5}}

The probability that actually there was head is P(A|X)={\frac{4}{5}}

Hence, option A is correct.

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