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佑信 發問時間: 科學數學 · 8 年前

Probability exercise

The probability that a married man watches a certain television show is 0.4, and the probability that a married woman watches the show is 0.5. The probability that a man watches the show, given that his wife does, is 0.7. Find the probability that

(a) a wife watches the show, given that her husband does;

(c) at least one member of a married couple will watch the show.

Answer:

(a)0.875 (b)0.55

請詳述計算過程, thx~

2 個解答

評分
  • 土扁
    Lv 7
    8 年前
    最佳解答

    Denotation :

    M = a married man watches the show

    W = a married woman watches the show

    Given :

    P(M) = 0.4

    P(W) = 0.5

    =====

    (a)

    P(M | W) = 0.7

    P(M and W) | P(W) = 0.7

    P(M and W) | 0.5 = 0.7

    P(M and W) = 0.35

    The required probability

    = P(W | M)

    = P(M and M) / P(M)

    = 0.35/0.4

    = 0.875

    =====

    (b)

    The required probability

    = P(M or W)

    = P(M) + P(W) - P(M and W)

    = 0.4 + 0.5 - 0.35

    = 0.55

    參考資料: 土扁
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  • mLee
    Lv 5
    8 年前

    The probability that a married man watches a certain television show is 0.4, and the probability that a married woman watches the show is 0.5. The probability that a man watches the show, given that his wife does, is 0.7. Find the probability that

    (a) a wife watches the show, given that her husband does;

    (b) at least one member of a married couple will watch the show.

    Let M be the event "a married man watches a certain TV show"

    P(M)=0.4

    Let W be the event "a married woman watches a certain TV show"

    P(W)=0.5

    P(M|W)=0.7

    P(M and W) / P(W) = 0.7

    P(M and W) = 0.7 * 0.5 = 0.35

    (a)

    P(W|M) = P(W and M) / P(M) = 0.35 / 0.4 = 7/8 = 0.875

    (b)

    P(M or W) = P(M) + P(W) - P(M and W) = 0.4 + 0.5 - 0.35 = 0.55

    參考資料: maeducation.edu.hk
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