MATHS more about probability

2009-03-16 6:24 am
In a certain industry , the probability that a worker suffers from occupational illness is 0.15 . If three workers of that industry are chosen at random ,find the probability that exactly two of them suffer from the illness.

希望大家詳細解答,,令我更加明白!!thx!!

回答 (2)

2009-03-16 6:38 am
✔ 最佳答案
Let 3 workers are A B C :
P(exactly two)
= P(A) * P(B) * P(notC) + P(A)*P(not B)*P(C) + P(not A)*P(B)*P(C)
= 0.15* 0.15 *(1-0.15) + 0.15*(1- 0.15)*0.15 +(1- 0.15)*(0.15)*(0.15)
= 3 * 0.15*0.15*0.85
= 0.057375



2009-03-15 23:29:36 補充:
題目要求計出不多不少恰好 2人病的概率,恰有2人病代表當中任何2人有病而另一人無病,這有3個情況 : A不病BC病,B不病AC病,C不病AB病,在現實中,這3個 cases 只能有一個會發生(互斥事件),因此三個case未發生前都有潛在可能,所以要用加法,把它們的可能性加總成為總體可能性。
2009-03-16 7:14 am
多謝你既答案...但係我唔明白點解要咁做??可唔可以有小小詳細解釋??thx!


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