統計學機率問題 (英文的題目)

[匿名]

2009-09-15 5:02 pm

According to the ABS, 20% of Australian households have a fax
machine and 66% of Australian households have a personal computer at home.

Suppose 91% of all Australian households with a fax machine also
have a personalcomputer. An Australian household is randomly selected.

問: What is the probability that the household has a fax machine and a
personal computer?

假設 F 是傳真機
C 是個人電腦 (ABS只是資料統計處)

ans: P( F and C ) = P(F )*P(C | F) = (0.20)*(0.91) = 0.182

為什麼要乘0.91,而不是答案直接是0.91?
(Suppose 91% of all Australian households with a fax machine also
have a personalcomputer.)

回答 (1)

Prof. Physics

2009-09-15 5:46 pm

✔ 最佳答案

因為題目給的條件是Suppose 91% of all Australian households with a fax machine also have a personal computer. P(C│F) 這是在有fax machine的家庭的條件下，再附加一個條件。

而不是91% of 所有澳洲家庭皆有personal computer

所以，在求機率時，應先求出有fax machine的機率，再在這條件下，乘上亦擁有電腦的機率

而不是只求有電腦的機率

因此，答案是

P(F and C)

= P(F)P(C│F)

= 0.20 X 0.91

= 0.182

=

參考: Physics king

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