In a game, a man wins ₹ 1000 if he gets an even number greater than or equal to 4 on a fair dice and loses ₹ 200 for getting any other number on the dice. If he decides to throw the dice until he wins or maximum of three times, then his exp

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In a game, a man wins ₹ 1000 if he gets an even number greater than or equal to 4 on a fair dice and loses ₹ 200 for getting any other number on the dice. If he decides to throw the dice until he wins or maximum of three times, then his expected gain/loss in (₹) is --

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Correct answer: B. 3800 9 gain

The outcomes on a fair dice are 1, 2, 3, 4, 5, 6 . Winning condition: Even number 4 , which are 4, 6 . Probability of winning p = 2 6 = 1 3 . Losing condition: Any other number, which are 1, 2, 3, 5 . Probability of losing q = 1 - p = 2 3 . The game stops if he wins or after 3 throws. Let X be the gain/loss. Case 1: Wins on 1st throw. Probability P₁ = p = 1 3 . Gain = 1000 . Case 2: Wins on 2nd throw. Probability P₂ = qp = 2 3 1 3 = 2 9 . Gain = -200 + 1000 = 800 . Case 3: Wins on 3rd throw. Probability P₃ = q^2p =

In a game, a man wins ₹ 1000 if he gets an even number greater than or equal to 4 on a fair dice and loses ₹ 200 for getting any other number on the dice. If he decides to throw the dice until he wins or maximum of three times, then his expected gain/loss in (₹) is --

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