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

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In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is :

(A) $\frac{400}{9}$ loss
(B)0✓ Correct
(C) $\frac{400}{3}$ gain
(D) $\frac{400}{3}$ loss

Answer: (B)

Solution

Winning (a

5

6

) has probability

\frac{1}{3}

, losing

\frac{2}{3}

, and play stops at the first win or after three throws. The outcomes with their gains are: win first,

\frac{1}{3}

+ 100

; lose then win,

\frac{2}{3} \cdot \frac{1}{3}

+ 50

; lose twice then win,

(\frac{2}{3})^{2} \cdot \frac{1}{3}

0

; lose all three,

(\frac{2}{3})^{3}

- 150

. The expectation is

\frac{1}{3} (100) + \frac{2}{9} (50) + \frac{4}{27} (0) + \frac{8}{27} (- 150) = \frac{900 + 300 - 1200}{27} = 0

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

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

Solution

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