2. 职称英语
  3. Quantity A: k is an integer between 1 and 100, inclusive what is probability tha

Quantity A: k is an integer between 1 and 100, inclusive what is probability tha

游客2024-01-12  72
问题 Quantity A: k is an integer between 1 and 100, inclusive what is probability that k×(k+1)×(k+2)×(k+3)×(k+4) is divisible by 20
Quantity B: 1
选项 A、Quantity A is greater.
B、Quantity B is greater.
C、The two quantities are equal.
D、The relationship cannot be determined from the information given.
答案 C
解析 k是从1到100的整数，包含1，100，对于表达式k×(k+1)×(k+2)×(k+3)×(k+4)来说，是5个连续的正整数相乘，5个连续的正整数中至少有两个连续的偶数，必然是4的倍数；5个连续的正整数中至少有一个是5的倍数。因此这个乘积必然能够被20整除，所以概率为1。选择C。
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