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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
admin
2021-10-21
45
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n
2
-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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