Karan tells truth with probability 1/3 and lies with probability 2/3. Independently, Arjun tells truth with probability 3/4 and lies with probability 1/4. Both watch a cricket match. Arjun tells you that India won, Karan tells you that India lost. What probability will you assign to India’s win?

# Conditional probability

**Mukul_d**#2

Probability India won = 1/2

Prob for India lost = 1/2

If definitely, India won : then

Arjun is telling the truth and karan is telling a lie then

arjun truth and karan lies = 3/4*2/3 = 1/2

arjun lies and karan truth = 1/4*1/3 = 1/2

Apply bayes therome now (1/2*1/2) /(1/2*1/2 + 1/2*1/12) = 6/7 is the answer

**Ruturaj**#4

There is a twist here actually. If the match is already over then you will assign probability of 1/2 to india’s win irrespective of the statements given by arjun and karan.

More appropriate question would have been, “*arjun tells you that india will win, karan tells you that india will loose*”.

In the above case we can go for bayes theorem and answer would be 6/7 as proposed by mukul_d.