2. 外语
  3. There are 10 packages of candy on a shelf, 4 that are filled with blue candies and 6 that are filled with red candies. If 3 pack

There are 10 packages of candy on a shelf, 4 that are filled with blue candies and 6 that are filled with red candies. If 3 pack

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问题 There are 10 packages of candy on a shelf, 4 that are filled with blue candies and 6 that are filled with red candies. If 3 packages are to be chosen at random from the shelf without replacement, what is the probability that at least one of the 3 packages will be filled with blue candies?
选项 A、11/12
B、5/6
C、3/4
D、2/3
E、7/12
答案B
解析 本题计算概率，先分清对分子和分母的不同描述。分母即总数，是10包糖中不放回地任取3包，即C103=120；分子即事件，是至少有一包糖是蓝色的，此时会发现若分类讨论到底有几包糖是蓝色，可能会分很多类，不如我们思考与之对立的情况，然后用总数减去对立的情况就是所求。“至少有一个是蓝色”的对立就是“一个蓝色都没有”，也就是“3包都是红色”，所以是C63=20。那么“至少有一个蓝色”有120-20=100种情况。所以最终所求概率为100/120=5/6。选择B选项。
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