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 P( E ), P( F ) and P( H ) be the probabilities that are defined below,

The probability that A speaks truth is P( E ).

The probability that A speaks lie is P( F ).

The probability that the head appears on the toss of a coin is P( H ).

The probability that the head actually appears, if A reports that a head appears that is P( E H ), P( E H )= P( E )P( H E ) P( F )P( H F )+P( E )P( H E ) (1)

Given that,

P( E )= 4 5

The probability that head appears, if A speaks truth,

P( H E )= 1 2

And

P( F )=1−P( E ) =1− 4 5 = 1 5

The probability that head appears, if A lies,

P( H F )= 1 2

Put these values in equation (1),

P( E H )= 4 5 × 1 2 1 5 × 1 2 + 4 5 × 1 2 = 4 5

Thus, correct option is (A).