Dear folks, please review where is the mistake with the following probability problem:

If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?

answ. said 5/8 but i got 1/8. where is the mistake?

n(n+1)(n+2) is consecutive integer and divisible by 8 is 8,16,24,32,40,48........96 (multiple number of 8)

thus, from 1 to 96 there are 12 number of 96 (12/96)--->1/8

thx

You have to choose n from 1-96 and not the product value as I think you are trying to do.

From n=1-96, all even numbers will satisfy the condition that n(n+1)(n+2) be divisible by 8 (try it out). There are 48 such numbers (96/2). In addition, odd numbers n such that n=8x-1 (i.e. 1 less than a multiple of 8) will also satify the condition. There are 12 such numbers (96/8). Total = 60 values of n that satisfy the condition.

Answer is 60/96 = 5/8.

pt,

thx for your explanation...
i've got it.

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