Question

A speaks truth in 80% cases and B speaks truth in 90%cases. In what percentage of cases are they likely to agree with each other in stating the same fact?

Answer 1

Explanation:

> Suppose A is the Event that A speaks the truth and B is the Event that B speaks the truth

=> According to the question, A speaks truth in 75% of cases and b in 80% of cases.

Thus, P(A) = 75% = 75/100 = 3/4

P(B) = 80% = 80/100 = 4/5

P(A-lie) = 1−34= 1/4

P(B-lie) = 1−45= 1/5

The percentage of cases in which they likely to contradict each other:

A and B contradict each other = [A true and B lies] or [A lies and B true]

= P(A).P(B-lie) + P(A-lie).P(B)

= (3/4 x 1/5)+(1/4 x 4/5)

= 3/20 + 4/20

= 3 + 4 / 20

= 7 / 20

% 0f cases in which A and B contradict each other = 7/20 * 100 = 35%