JEE MAIN - Mathematics (2019 - 12th April Evening Slot - No. 17)
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 :
$${1 \over 4}$$ loss
$${1 \over 2}$$ gain
$${1 \over 2}$$ loss
2 gain
Explanation
When two dice are thrown then sample space will {(1, 1), (2, 2) ....... (6, 6)} contain total 36 elements number of cases.
Then the expectation will be $${6 \over {36}} \times 15 \times {4 \over {36}} \times 12 - {{26} \over {36}} \times 6$$
$${{90 + 48 - 156} \over {36}} = - {1 \over 2}$$ = $$ {1 \over 2}$$ loss
Then the expectation will be $${6 \over {36}} \times 15 \times {4 \over {36}} \times 12 - {{26} \over {36}} \times 6$$
$${{90 + 48 - 156} \over {36}} = - {1 \over 2}$$ = $$ {1 \over 2}$$ loss
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