The probabilities that A and B will tell the truth are 2 / 3 and 4 / 5 respectiv

CuriousTab

Home Aptitude

Question
The probabilities that A and B will tell the truth are 2 / 3 and 4 / 5 respectively . What is the probability that they agree with each other ?
Options
A. 3/5
B. 1/3
C. 2/5
D. 3/4

Correct Answer

3/5

Explanation

Let A be the event of A will tell truth. B be the event of B tell truth

$P (A) = \frac{2}{3}, P (A^{c}) = 1 - P (A) = \frac{1}{3}$

$P (B) = \frac{4}{5}, P (B^{c}) = 1 - P (B) = \frac{1}{5}$

When both agree then they say true or they say false together, that is

$A ? B o r A^{c} ? B^{c}$

Also these events will be mutually exclusive :

$P (A ? B) + P (A^{c} ? B^{c}) = P (A) P (B) P (C) = \frac{2}{3} * \frac{4}{5} + \frac{1}{3} * \frac{1}{5} = \frac{3}{5}$