tiger asked in 科學數學 · 1 decade ago

統計機率問題忘了怎麼算

設單一試驗成功機率為0.3,今做兩次試驗,結果至少成功一次的機率為何?

A.0.910

B.0.20

C.0.510

D.0.490

E.0.030

會的幫我解一下.越詳細越好

3Q

1 Answer

Rating
  • 1 decade ago
    Favorite Answer

    有兩個方法可做。

    1. P(至少成功一次)

    = 1 - P(兩次皆不成功)

    = 1 - (1 - 0.3)2

    = 1 - 0.72

    = 1 - 0.49

    = 0.510

    答案是C

    2. P(至少一次成功)

    = P(第一次成功及第二次失敗) + P(第一次失敗及第二次成功) + P(兩次皆成功)

    = 0.3 X (1 - 0.3) + (1 - 0.3) X 0.3 + 0.3 X 0.3

    = 0.21 + 0.21 + 0.09

    = 0.510

    答案是C

    注意「兩次皆不成功」與「至少一次成功」是mutually exclusive events,即兩者不能同時發生的,而相加的機率 = 1

    Source(s): Physics king
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