PROBABILTY

your three integers are consecutive so there are two basic possibilities

if n is even, both n and n+2 are even. Also, one of them must be divisible by 4, so the product will be divisible by 8. That happens 48 times.

if n is odd, you have 2 odd numbers and one even number. For the product to be divisible by 8,the one even number (the middle one) must be divisible by 8. that will happen if n = 7,15,23,31,39,47,55,63,71,79,87 or 95 ( 12 times)

Total = (48+12)/96 = 60/96 = 5/8

Tani Wolff - Kaplan wrote:your three integers are consecutive so there are two basic possibilities

if n is even, both n and n+2 are even. Also, one of them must be divisible by 4, so the product will be divisible by 8. That happens 48 times.

if n is odd, you have 2 odd numbers and one even number. For the product to be divisible by 8,the one even number (the middle one) must be divisible by 8. that will happen if n = 7,15,23,31,39,47,55,63,71,79,87 or 95 ( 12 times)

Total = (48+12)/96 = 60/96 = 5/8

Wow, good answer. I got 1/2 after thinking it only applied to even numbers. Didn't think to have other options where the number has 8 in it.

how do you get 48 times in the first instance and 12 in the next
other than counting the numbers what is the approach

Tani Wolff - Kaplan wrote:your three integers are consecutive so there are two basic possibilities

if n is even, both n and n+2 are even. Also, one of them must be divisible by 4, so the product will be divisible by 8. That happens 48 times.

if n is odd, you have 2 odd numbers and one even number. For the product to be divisible by 8,the one even number (the middle one) must be divisible by 8. that will happen if n = 7,15,23,31,39,47,55,63,71,79,87 or 95 ( 12 times)

Total = (48+12)/96 = 60/96 = 5/8

The first list refers to groups of three consecutive numbers, each of which starts with an even number. There are 48 even number from 1-96 inclusive (simply divide 96 by 2).

For the second list, you have to have the middle number be divisible by 8. Dividing 96 by 8 you can see there are twelve numbers between 1 and 96 inclusive that are divisible by 8.