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  3. Three red marbles and 2 white marbles are placed in an empty box. One marble at

Three red marbles and 2 white marbles are placed in an empty box. One marble at

游客2025-02-24  9
问题 Three red marbles and 2 white marbles are placed in an empty box. One marble at a time is to be selected randomly and removed from the box until all 5 marbles have been removed. What is the probability that each of the first 3 marbles removed will be red?
选项 A、1/32
B、1/20
C、1/10
D、1/2
E、3/5
答案 C
解析 一个空盒子中放有3个红色弹珠和2个白色弹珠，每次随机取出1个弹珠并且直到5个弹珠都被取出来。问取出的前3个弹珠全部是红色的概率有多大?
解：本题的正确答案是(C)。第一次取出红色弹珠的概率为3/5；第一次取出后，盒子中剩2红2白，因此第二次取出红色弹珠的概率为2/4；第二次取出后盒子中剩2白1红，因此第三次取出红色弹珠的概率为1/3。前三次取出的球都是红球的概率是每次取出的球都是红球的概率的乘积，即3/5×2/4×1/3=1/10
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