Suppose x and y are selected randomly from the set {1, 2, 3, 4, 5} and they can repeat. What is the probability that xy+y is odd

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问题 Suppose x and y are selected randomly from the set {1, 2, 3, 4, 5} and they can repeat. What is the probability that xy+y is odd?

选项

答案0.24

解析由xy+y是奇数，可以推出xy和y是一奇一偶。若y是偶数，z是奇数，xy+y是偶数，不符合题意。若y是奇数，x是偶数，xy+y是奇数，符合题意。接下来就要从(1，2，3，4，5)中选1个奇数和1个偶数。(1，2，3，4，5}中一共有2个偶数，3个奇数。因此x有2个选择：2、4；y有3个选择：1、3、5。则用乘法原理算出xy+y是奇数的情况有2×3=6种。不考虑奇偶性，则总的选择有5×5=25种。所以，概率P=6/25=0.24。

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