2016 AMC 10A Problems/Problem 12
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?
Solution
There are an equal amount of even and odd numbers from through
. This concludes that the probability of choosing an even number is the same of that of choosing an odd number. The only way to get a product of three integers to be odd is for all three integers to be odd. If the probability of choosing an odd number is
, then the probability of choosing
odd numbers would be
Therefore, the answer is
.