Anil and Bhavna play a game in which a fair coin is tossed twice. Anil wins if at least one head appears; otherwise Bhavna wins. Bhavna pays Anil ₹9 whenever Anil wins. How much must Anil pay Bhavna whenever she wins, in ₹, for the game to be fair to both?

Question

Accepted Answer

27. Anil wins with probability 3/4, since only TT loses, and Bhavna wins with probability 1/4. Anil's expected gain is (3/4)(9) − (1/4)y, which is zero when (1/4)y = 27/4, that is y = 27. The rarer win must carry the bigger stake; equal stakes of ₹9 would leave Anil ₹4.50 ahead per game on average.

Anil and Bhavna play a game in which a fair coin is tossed twice. Anil wins if at least one head appears; otherwise Bhavna wins. Bhavna pays Anil ₹9 whenever Anil wins. How much must Anil pay Bhavna whenever she wins, in ₹, for the game to be fair to both?

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Data & Probability practice