PYQ Vault

Expected gain or loss in a game of chance

This type of question, asked 6 times: 3 May 2023 S1, 10 May 2023 S1, 10 May 2024 S2, 19 Apr 2025 S2, 23 Apr 2025 S1, 19 Apr 2026 S1. All 6 questions below, oldest first.

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  1. Question 1

    3 May 2023 S1

    140
    A person throws an unbiased die. If the number shown is even, he gains an amount equal to the number shown. If the number is odd, he loses an amount equal to the number shown. Then his expectation is Rs.

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  2. Question 2

    10 May 2023 S1

    107
    In a game, 3 coins are tossed. A person is paid ₹100, if he gets all heads or all tails; and he is supposed to pay ₹40, if he gets one head or two heads. The amount he can expect to win/lose on an average per game in (₹) is

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  3. Question 3

    10 May 2024 S2

    137
    In a game, 3 coins are tossed. A person is paid ₹7 if he gets all heads or all tails; and he is supposed to pay ₹3 if he gets one head or two heads. The amount he can expect to win on an average per game is

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  4. Question 4

    19 Apr 2025 S2

    123
    In a game, 3 coins are tossed. A person is paid ₹150 if he gets all heads or all tails and he is supposed to pay ₹50 if he gets one head or two heads. The amount he can expect to win / lose on an average per game in ₹ is

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  5. Question 5

    23 Apr 2025 S1

    113
    In a game a man wins ₹ 40 if he gets 5 or 6 on a throw of a fair die and loses ₹ 20 for getting any other number on the die. If he decides to throw the die either till, he gets a five or six or to a maximum of three throws, then his expected gain/loss (in rupees) is

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  6. Question 6

    19 Apr 2026 S1

    100
    Consider a game of tossing a six sided fair die. If the face that comes up is 66, the player wins Rs. 3636 and he loses Rs. k2k^2, where kk is the face that comes up k={1,2,3,4,5}k = \{1, 2, 3, 4, 5\}, then the expected winning amount in this game in Rs. is...

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