Re: [問題] 條件機率的計算
※ 引述《ChrisOvO (YOMAN)》之銘言：
: 題目是這樣子的:
: The probability that,on the weekday,the college will receive letters addressed to Dr.A is 1/3. Dr.A,who arrives earlier than any of his colleagues,begins the day by collecting his mail. He has told me that there is 40% chance that he will attend college today;and I have noticed that there are no letters in his pigeon hole.In view of there being no mail in his box,what is the probability that he is attending today?
: http://miupix.cc/pm-6UFKAJ
: 圖片上面是我的想法:
: 令A表是他有到學校
: R表示他有收到信
: 當他到學校時，收到信的機率就是1/3
: 而如果他沒到學校，就不會收到信
: 但解答的想法卻是下面的那樣
: 跟我的想法似乎相反
: 想問我的想法錯在哪呢？
http://ppt.cc/9KK9
你看不到信的前提下 他有沒有來
所以在看不到信的情況下他有來的機率應該是這樣算
應該是以有信跟沒信開始
1/3*2/5=2/15 (有信有來 你看不到信)
2/3*2/5=4/15 (沒信有來 你看不到信)
2/3*3/5=6/15 (沒信沒來 你看不到信)
所以你看不到信的機率為 12/15=4/5
看不到信但是有來的機率為 6/15
所以條件機率為
(6/15) / (4/5) = 1/2
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