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CA Foundation · Quantitative Aptitude · Probability

A game at a Jaipur fair costs Rs 20 to play. A player tosses two fair coins and receives Rs 50 if both show heads, Rs 20 if exactly one shows head, and nothing if both show tails. What is the player's expected net gain per play?

The expected net gain is Rs 2.50. The expected payout is 50 times 1/4 plus 20 times 1/2, which equals Rs 22.50. Subtracting the Rs 20 entry fee leaves a positive expected gain of Rs 2.50 per play.

  1. ARs 2.50Correct
  2. BRs 0
  3. CRs -7.50
  4. DRs 7.50

Explanation

P(2H)=1/4, P(1H)=1/2, P(0H)=1/4. Expected payout = 50(1/4)+20(1/2)+0 = 12.5+10 = 22.5. Net gain = 22.5 - 20 = Rs 2.50. Rs 22.50 would be wrongly ignoring the entry fee.

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