CareerCup

there are two cases in which india win:
1) Akbar tells the truth and Amar tells the truth : 3/4*3/4 = 9/16
2) Akbar tells a lie that India loose and Amar tells lie to anthony that "Akbar told me india win" : 1/4*1/4 = 1/16

So total probability of winning India would be 9/16 + 1/16 = 10/16

Correct me if I am wrong.

None of the above. There are basically 8 case. Truth->Amar->Akbar. (2)(2)(2). We do not know the probability of India Winning (let it be x). So the 4 cases we should consider is (truth, amar, akbar) WWW (x*(3/4)^2), WLW(x*(3/4)*(1/4)),LWW((1-x)*(1/4)^2),LLW ((1-x)*(3/4)*(1/4))= (x/2)+(1/4).

For which company was this interview?

1/4*1/4+3/4*3/4=1/16+9/16=10/16

Well, the answer's right, the method's wrong. Based on Akbar telling Anthony that "Amar says India has won", Anthony would actually consider 4 cases:

India actually won: (Prob = 0.5)
1. Amar tells truth, Akbar tells truth (Prob = 9/16)
2. Amar lies, Akbar lies (Prob = 1/16)

India actually loses: (Prob = 0.5)
1. Amar tells truth, Akbar lies (Prob = 3/16)
2. Amar lies, Akbar speaks truth (Prob = 3/16)

Bayes theorem:
(9/16 + 1/16) / ((9/16 + 1/16) + (3/16 + 3/16)) = 10/16

What about the probability of Amar telling what the outcome is i.e., Pr(Amar telling Akbar that India won/lost), since we do not know what Amar told Akbar.
So, shouldn't it then be Pr(Amar telling Akbar India won) * Pr(Amar telling the truth)* Pr(Akbar telling the truth) = 1/2*3/4*3/4
+
Pr(Amar telling Akbar India lost) * Pr(Amar telling a lie)* Pr(Akbar telling a lie) = 1/2*1/4*1/4
i.e. total Pr = 1/2(9/16+1/16) = 1/2*10/16 = 5/16?

9/16