Question

A speaks truth in 75% of the cases, while B in 90% of the cases. In what percent of cases are they likely to contradict each other in stating the same fact? Do you think that statement of B is true?

Answer 1

Let A be the event that A speaks the truth.

Let B be the event that B speaks the truth.


Given that A speaks the truth in 75% of the cases.

 P(A) = 75/100

         = 3/4.

Given that B speaks the truth in 90% of the cases.

P(B) = 90/100

       = 9/10.


(1) When A doesn't speak the truth and B speak the truth.

      = (1 - P(A)) * P(B)

      = (1 - 3/4) * 9/10

      = 1/4 * 9/10

      = 9/40.


(2) When A speak truth and B don't speak the truth.

    = P(A) * (1 - P(B))

   = 3/4 * (1 - 9/10))

   = 3/4 * 1/10

   = 3/40.


Now, we need to find the % of cases in which they are likely to contradict      

 = (9/40 + 3/40) * 100

 = 12/40 * 100

= 30%.


Therefore A and B contradict each other in 30% of the cases and B speaks the truth in most of the cases.


Hope this helps!                         

Answer 2

Answer:

30% Aand B will contradict