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Expected number of special items (defectives, green balls, queens) drawn without replacement

This type of question, asked 3 times: 11 May 2024 S1, 20 Apr 2025 S1, 17 Apr 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    11 May 2024 S1

    104
    From a lot of 20 baskets, which includes 6 defective baskets, a sample of 2 baskets is drawn at random one by one without replacement. The expected value of number of defective baskets is

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  2. Question 2

    20 Apr 2025 S1

    119
    Two cards are drawn simultaneously from a well shuffled pack of 52 cards. If X is the random variable of getting queens, then the value of 2E(X)+3E(X2)2E(X) + 3E\left( X^{2} \right) for the number of queens is

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  3. Question 3

    17 Apr 2026 S1

    100
    A box contains 8 red and N green balls. Two balls are drawn at random from it. If X is the random variable representing the number of green balls drawn and E(X)=1.2E(X) = 1.2, then N=…N = \ldots

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