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JEE Main 2019 · 12 April · Shift II

JEE Main 2019 Mathematics question on Probability

A person throws two fair dice. He wins ₹ 15 for throwing a doublet (same numbers on the two dice), wins ₹ 12 when the throw results in the sum of 9, and loses ₹ 6 for any other outcome on the throw. Then, the expected gain/loss (in ₹) of the person is
  1. A.
    12\frac{1}{2} gain
  2. B.
    14\frac{1}{4} loss
  3. C.
    12\frac{1}{2} loss
  4. D.
    2 gain
Show answer and solution

Correct option: C

Solution

Doublets: 6 outcomes out of 36, probability = 6/36 = 1/6.
Sum of 9 (non-doublet): (3,6),(6,3),(4,5),(5,4) = 4 outcomes, probability = 4/36 = 1/9.
Other outcomes: 36 - 6 - 4 = 26, probability = 26/36 = 13/18.

Expected gain = 15·(1/6) + 12·(1/9) + (-6)·(13/18)
= 15/6 + 12/9 - 78/18
= 45/18 + 24/18 - 78/18
= (45 + 24 - 78)/18
= -9/18 = -1/2.

The negative sign indicates a loss of ₹ 1/2, confirming option 3.

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