Question

Two dice are thrown simultaneously. Find the probability that the sum of numbers on the faces is neither divisible by 4 and nor by 5.​

Answer 1

ANSWER:-

The sample space S when two dice are thrown together is:

(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6). 

Therefore, n(S)=36.

Let A denote the event that sum of number is not divisible by 4 or 5 that is: 

(1,1),(1,2),(1,5),(1,6),(2,1),(2,4),(2,5),(3,3),(3,4),(3,6),(4,2),(4,3),(4,5),(5,1),(5,2),(5,4),(5,6),(6,1),(6,3),(6,5)

n(A)=20, therefore, probability that sum of number is not divisible by 4 or 5 is:

P(A)=n(S)n(A)=3620=95

Hence, probability that sum of number on the faces is neither divisible by 4 nor by 5 is 5/9 (5 by 9)