Question

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

A.

B.

C.

D.

Answer 1

Let E₁ and E₂ be the events such that

E₁: A speaks truth

E₂: A speaks false

Let X be the event that a head appears.
$P\left(E_1\right)=\frac{4}{5}$
Therefore,
$P\left(E_2\right)=1-P\left(E_1\right)=1-\frac{4}{5}=\frac{1}{5}$

If a coin is tossed, then it may result in either head (H) or tail (T).

The probability of getting a head is whether A speaks truth or not.

The probability that there is actually a head is given by P (E₁|X).

Therefore, the correct answer is A.