Question:
A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins Rs. 12 when the throw results in the sum of 9, and loses Rs. 6 for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is :
A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins Rs. 12 when the throw results in the sum of 9, and loses Rs. 6 for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is :
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Count the favourable outcomes for each payoff out of 36 and compute the expected value \(\sum p_i x_i\).
Updated On: Nov 11, 2026
- \(\frac{1}{4}\) loss
- \(\frac{1}{2}\) gain
- \(\frac{1}{2}\) loss
- 2 gain
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The Correct Option is C
Solution and Explanation
Total outcomes = 36.
Doublets: (1,1),...,(6,6) = 6 outcomes, gain Rs. 15. Sum 9: (3,6),(6,3),(4,5),(5,4) = 4 outcomes (none is a doublet), gain Rs. 12.
Other outcomes = 36 - 6 - 4 = 26, gain \(-6\).
\(E = \frac{6}{36}(15)+\frac{4}{36}(12)+\frac{26}{36}(-6) = \frac{90+48-156}{36} = \frac{-18}{36} = -\frac{1}{2}\).
Negative expected value means a loss of Rs. \(\frac{1}{2}\).
Answer: (3) \(\frac{1}{2}\) loss
Doublets: (1,1),...,(6,6) = 6 outcomes, gain Rs. 15. Sum 9: (3,6),(6,3),(4,5),(5,4) = 4 outcomes (none is a doublet), gain Rs. 12.
Other outcomes = 36 - 6 - 4 = 26, gain \(-6\).
\(E = \frac{6}{36}(15)+\frac{4}{36}(12)+\frac{26}{36}(-6) = \frac{90+48-156}{36} = \frac{-18}{36} = -\frac{1}{2}\).
Negative expected value means a loss of Rs. \(\frac{1}{2}\).
Answer: (3) \(\frac{1}{2}\) loss
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