Suppose x and y are selected randomly from the set {1, 2, 3, 4, 5} and they can

游客2024-01-12  23

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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