Question

Probability that A speaks truth is $\frac{4}{5}$.A coin is tossed.A report 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. ($\frac{2}{5}$)

Answer 1

Answer: (A)

($\frac{4}{5}$)

Answer 2

Let A be the event that the man reports that head occurs in tossing a coin and let E1 be the event that head occurs and E2 be the event head does not occur.
P(E1)=$\frac{1}{2}$,P(E2)=$\frac{1}{2}$
P(A|E1)=P(A reports that head occurs when head had actually occur red on the coin)=$\frac{4}{5}$
P(A|E2)=P(A reports that leads occurs when head had not occur red on the coin)=1-$\frac{4}{5}$=$\frac{1}{5}$
By Bayes'theorem,
P(E1|A)=$\frac{P(E1)P(A|E_1)}{P(E_1)P(A|E_1)+P(E_2)P(A|E_2)}$=$\frac{\frac{1}{2}×\frac{4}{5}}{\frac{1}{2}×\frac{4}{5}+\frac{1}{2}×\frac{1}{5}}$=4/4+1=4/5
Hence,option (A) is correct.