- AThe game is unfair; the player loses ₹0.25 per game on average
- BThe game is fair, because a win pays more than a loss costs
- CThe game is unfair; the player gains ₹0.25 per game on average
- DThe game is unfair; the player loses ₹3 per game on average
Step-by-Step Solution
All three coins match in 2 of the 8 equally likely outcomes, HHH and TTT, so the win probability is 2/8 = 1/4. The expected gain is (1/4)(5) + (3/4)(−2) = 1.25 − 1.50 = −0.25, a loss of ₹0.25 per game on average. A bigger prize does not by itself make a game fair — the prize has to be weighed by how often it is won. For fairness the prize would have to be ₹6, since (1/4)(6) = (3/4)(2).
Answer: A) The game is unfair; the player loses ₹0.25 per game on average