CA Foundation · Quantitative Aptitude · Probability
A game at a Jaipur fair costs Rs 20 to play. A fair coin is tossed twice. The player gets Rs 40 if two heads appear, Rs 20 if exactly one head appears, and nothing if no head appears. What is the player's expected net gain per game?
The expected payout is Rs 20, from 40 times 1/4 plus 20 times 1/2. The entry fee is also Rs 20, so the expected net gain is zero and the game is fair.
- ARs 0
- BRs 5Correct
- CRs -5
- DRs 10
Explanation
P(2H)=1/4, P(1H)=1/2, P(0H)=1/4. Expected payout = 40(1/4)+20(1/2)+0 = 10+10 = Rs 20. Net gain = 20 - 20 = 0. Rs 20 is the expected payout, not the net gain; Rs 5 comes from wrongly using 1/4 for one head.
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