In a game, a person is paid Rs. 2 if he gets all heads or all tails when three coins are tossed, and he will pay Rs. 2 if either one or two heads show. What can he expect to win on an average per game?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Lose Rs. 1 per toss of the coins.
Three coins give 8 equally likely outcomes. All heads or all tails (HHH, TTT) is 2 of them; one or two heads is the other 6.
Let X be his gain in rupees:
\(P(X = 2) = \frac{2}{8} = \frac{1}{4}\)
\(P(X = -2) = \frac{6}{8} = \frac{3}{4}\)
The expected value is
\( \displaystyle E(X) = 2 \times \frac{1}{4} + (-2) \times \frac{3}{4} = \frac{1}{2} - \frac{3}{2} = -1 \)
So on average he loses Rs. 1 per game.