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匿名 發問於 科學及數學數學 · 4 月前

Probability Problem? ?

Q1) A bag contains 3 red balls and 2 blue balls. A ball is taken at random from the bag. If the ball is blue, it is taken out of the bag, and otherwise, it is left in. A second ball is drawn from the bag. What is the probability that the first ball drawn is blue, given the second drawn was red? 

Q2)  A bag contains 3 red balls and 2 blue balls. A ball is taken at random from the bag. If the ball is blue, it is taken out of the bag, and otherwise, it is left in. A second ball is drawn from the bag. What is the probability that both the first and second ball drawn are red? 

1 個解答

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  • 4 月前
    最愛解答

    Q1) 

    設事件 E 代表 the first ball drawn is blue,

    事件 F 代表 the second drawn is red.

    P{E∩F} = 2/5 × 3/4 = 3/10

    P{F} = P{E∩F} + P{E'∩F}

            = 2/5 × 3/4 + 3/5 × 3/5 = 33/50

    ∴ P{E|F} = (3/10) ÷ (33/50) = 5/11

    Q2) 

    設事件 E' 代表 the first ball drawn is red,

    事件 F 代表 the second drawn is red.

    E' 發生時, 袋中球維持不變, 故 P{F|E'} = P{E'}.

    ∴ P{E'∩F} = 3/5 × 3/5 = 9/25

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