Question

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 ______.

Options

• `1/2` gain

• `1/4` loss

• `1/2` loss

• 2 gain

Answer 1

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 `underlinebb(1/2 loss)`.

Explanation:

Let X be the random variable which denotes the Rs gained by the person.

Total cases = 6 × 6 = 36.

Favourable cases for the person winning ₹ 15 are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6) i.e., 6 cases.

∴ P (X = 15) = `6/36 = 1/6`

Favourable cases for the person winning ₹ 12 are (6, 3), (5, 4), (4, 5), (3, 6) i.e., 4.

∴ P (X = 12) = `4/36 = 1/9`

Remaining cases = 36 – 6 – 4 = 26

∴ P (X = – 6) = `26/36 = 13/18`

X	15	12	– 6
P (X)	`1/6`	`1/9`	`13/18`
X . P (X)	`5/2`	`4/3`	`(-13)/3`

Hence E (X) = `sumX . P(X) = 5/2 + 4/3 - 13/3 = -1/2`