A random number N is chosen from 1 to 96 inclusive, what is the probability that the number N(N+1)(N+2) is divisible by 8?
5/8 ?simplythebest wrote:A random number N is chosen from 1 to 96 inclusive, what is the probability that the number N(N+1)(N+2) is divisible by 8?
If n is even, then n*(n+2) will yield a product which is a multiple of 8. So,
1/2 the numbers will satisfy this.
If n is odd, the condition will be satisfied when n+1 is a multiple of 8.
There is 1 such number for every 4 consecutive odd numbers (7,
15, 23 etc.).
So, total = 1/2 + 1/2*1/4 (where 1/2 is probability of odd and
1/4 is probability of n+1 being multiple of 8 in the list of odd integers).
So, 1/2 + 1/8 = 5/8
