Question 1204981
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If n is even, then n+2 is even, and one of them (exactly one of them) is a multiple of 4.  So together the first and last of the three consecutive integers have 3 factors of 2, which makes the product divisible by 8.<br>
Half of the numbers 1 through 96 are even, so the probability is 1/2 that n is even and the product is divisible by 8.<br>
If n is odd, then n+2 is odd; for the product of the three consecutive integers to be divisible by 8, the middle number has to be divisible by 8.  Since 1 out of every 8 integers from 1 to 96 is divisible by 8, the probability is 1/8 that n is odd and the product is divisible by 8.<br>
The two cases of n even and n odd cover all possibilities, so the probability that the product is divisible by 8 is<br>
ANSWER: 1/2 + 1/8 = 5/8<br>