Question:
In a game, 3 coins are tossed. A person is paid Rs \( 150 \) if he gets all heads or all tails and he is supposed to pay ₹\( 50 \) if he gets one head or two heads. The amount he can expect to win lose on an average per game in ₹ is
In a game, 3 coins are tossed. A person is paid Rs \( 150 \) if he gets all heads or all tails and he is supposed to pay ₹\( 50 \) if he gets one head or two heads. The amount he can expect to win lose on an average per game in ₹ is
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A fair game is one where the expected value of the winnings is zero.
Updated On: May 12, 2026
- 100
- 0
- 200
- -100
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Concept
Expected value $E(X) = \sum X \cdot P(X)$.
Step 2: Meaning
Total outcomes for 3 coins = 8. All heads (HHH) or all tails (TTT) occurs in 2 cases. One or two heads occur in $8 - 2 = 6$ cases.
Step 3: Analysis
$P(\text{Win } 150) = 2/8 = 1/4$. $P(\text{Lose } 50) = 6/8 = 3/4$. $E(X) = (150 \times 1/4) + (-50 \times 3/4) = 37.5 - 37.5 = 0$.
Step 4: Conclusion
The average amount expected is ₹0, meaning it is a fair game. Final Answer: (B)
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