求解答probability

Nickname

2012-07-25 7:18 pm

A 3-digit integer formed from 0,1,3,5,7,9 without repetition, find the prob. that the integer can be divided by 5. (答案：0.36)

5 MC questions each with4 choices， a student answer all questio by guessing, find the prob. that the student get exactly 2 questions correct.(答案：0.26)

我想知道為什麼答案會是這樣，可以的話我想看看列式是怎麼樣OTZ

回答 (1)

用戶2053

2012-07-25 7:55 pm

✔ 最佳答案

1) The last digit must be 0 or 5.Case 1 :
XX0
XX 是由 1,3,5,7,9 抽2個的一個排列 , 共 5P2 = 5 * 4 = 20 種。Case 2 :
XX5
XX 是 0,1,3,7,9 的一個排列 ,
由於第一個X不為0 , 第一個X共4個choices ,
第二個X可為0 , 加上1,3,7,9 未選的3個共4個choices,
共 4 * 4 = 16 種。There are 20 + 16 = 36 cases can be divided by 5.而 0,1,3,5,7,9 共可組成 5 * 5 * 4 = 100 個 3-digit integers , 所以 the prob. = 36/100 = 0.36。

2) P(exactly 2 questions correct)= 5C2 * (1/4)(1/4)(3/4)(3/4)(3/4)= 10 * 27/1024 = 0.26

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