# 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 - Mathematics

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

#### Solution

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(E1)=45
Therefore,
P(E2)=1-P(E1)=1-45=15

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

The probability of getting a head is 1/2 whether A speaks truth or not.

:.P(X|E_1) = P(X|E_2) = 1/2

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

Is there an error in this question or solution?

#### APPEARS IN

NCERT Class 12 Maths
Chapter 13 Probability
Q 13 | Page 557