2. 外语
  3. Five red balls and two blue balls are placed in all empty box. One ball a time is to be selected randomly and removed 4 balls fr

Five red balls and two blue balls are placed in all empty box. One ball a time is to be selected randomly and removed 4 balls fr

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问题 Five red balls and two blue balls are placed in all empty box. One ball a time is to be selected randomly and removed 4 balls from the box. What is the probability that the first two balls removed will be red and the third ball removed will be blue?
选项 A、4/21
B、4/7
D、5/7
E、2/5
答案A
解析 第一次取出红球的概率为5/7，第二次取出红球的概率为4/6，第三次取出蓝球的概率为2/5，利用乘法原理得到所求概率为=421，注意这道题目和直接从盒子中取出3个球(2红1蓝)的概率是有区别的，后者刚好是前者的3倍。如果用代入法来做最简单，比如随便选择一个奇数3，9-1=8，因此除以8余数为0。如果按照原理来做，则是n2-1=(n-1)(n+1)，由于n是奇数，所以n-1和n+1是两个连续的正偶数，两个连续的正偶数的乘积必然是8的倍数，所以除以8余数为0。选择B。
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