Problem:
Three distinct integers are selected at random between and , inclusive. Which of the following is a correct statement about the probability that the product of the three integers is odd?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The product of three integers is odd if and only if all three integers are odd. There are odd integers among the integers in the given range. The probability that all the selected integers are odd is
The first factor is and each of the other factors is less than , so .
The problems on this page are the property of the MAA's American Mathematics Competitions