JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Probability

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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) $\frac{1}{4}$ loss
(B)2 gain
(C) $\frac{1}{2}$ gain
(D) $\frac{1}{2}$ loss✓ Correct

Answer: (D)

Solution

Out of

36

equally likely throws,

6

are doublets (win

15

), and the four ways to total

9

, namely

(3, 6), (4, 5), (5, 4), (6, 3)

, win

12

; the remaining

26

lose

6

. The expected value is

\frac{1}{36} [6 (15) + 4 (12) + 26 (- 6)] = \frac{90 + 48 - 156}{36} = \frac{- 18}{36} = - \frac{1}{2}

, a loss of half a rupee.

JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Single correct option

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