Probability that A speaks truth is (4/5).A coin is tossed. A reports that a head appears. The probability that actually there was head is

Question

Probability that A speaks truth is (4/5).A coin is tossed. A reports that a head appears. The probability that actually there was head is (A) (4/5) (B) (1/2) (C) (1/5) (D) (2/5)

Tardigrade Admin · Accepted Answer

P(E1)=P(E2)=(1/2) P(B / E1)=(4/5) B: A reports head P(B / E2)=(1/5) P(E1 / B)=((4/5) × (1/2)/(4)5 × (1)2+(1/5) × (1/2)=(4/5)

Q. 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

$\frac{4}{5}$

$\frac{1}{2}$

$\frac{1}{5}$

$\frac{2}{5}$

$P (E_{1}) = P (E_{2}) = \frac{1}{2} P (B / E_{1}) = \frac{4}{5}$
$B : A$ reports head $P (B / E_{2}) = \frac{1}{5}$
$P (E_{1} / B) = \frac{\frac{4}{5} \times \frac{1}{2}}{\frac{4}{5} \times \frac{1}{2} + \frac{1}{5} \times \frac{1}{2}} = \frac{4}{5}$

Q. Probability that A speaks truth is 54​.A coin is tossed. A reports that a head appears. The probability that actually there was head is

54​

21​

51​

52​