# Moderate Probability Solved QuestionAptitude Discussion

 Q. Dinesh speaks truth in 3/4 cases and Abhishek lies in 1/5 cases. What is the percentage of cases in which both Dinesh and Abhishek contradict each other in stating a fact?
 ✖ A. 60% ✔ B. 35% ✖ C. 20% ✖ D. 15%

Solution:
Option(B) is correct

D and A will contradict each other when one speaks truth and other speaks lies.

Probability of D speak truth and A lies

$=\dfrac{3}{4}\times \dfrac{1}{5}$

$=\dfrac{3}{20}$

Probability of A speak truth and D lies

$=\dfrac{4}{5}\times \dfrac{1}{4}$

$=\dfrac{1}{5}$

The two probabilities are mutually exclusive.
Hence, probabilities that D and A contradict each other:

$=\dfrac{3}{20}+\dfrac{1}{5}$

$=\dfrac{7}{20}$

$=0.35 \times 100\%$

$=35\%$

## (1) Comment(s)

Steve
()

I think you are not taking into account the possibility that the could both not tell the truth and yet contradict each other. they could both lie and still contradict each other.