mathQ(probability)

[匿名]

2009-03-23 9:06 pm

In a swimming pool,70% of the swimmers are male. It is known
that 20% of the male swimmers and 60% of the female
swimmers wear swimming caps. Given that two swimmers wear swimming caps,find the probability that one of them is a male
swimmer. Given your answer correct to decimal places.
Ans=0.49

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回答 (1)

Prof. Physics

2009-03-23 9:36 pm

✔ 最佳答案

First of all, let's consider the tree-diagram.

圖片參考：http://i726.photobucket.com/albums/ww265/physicsworld2010/physicsworld01Mar231331.jpg?t=1237786357

P(a swimmer wears swimming cap)

= (0.7)(0.2) + (0.3)(0.6)

= 0.32

P(two swimmers wear swimming caps)

= (0.32)2

= 0.1024

The required probability

= P(one is male and one is female│two wearing caps)

= P(one male and one female wearing caps) / P(two swimmers wear caps)

= [2 X (0.7)(0.2) X (0.3)(0.6)] / 0.1024

= 0.49 (cor. to 2 d.p.)

參考: Physics king

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