Two dices were thrown simultaneously What is the probability that the sum of the two numbers appearing on - Maths - Probability

Question

Two dices were thrown simultaneously What is the probability that
the sum of the two numbers appearing on the top of the dice is less
than 10 and is not divisible by 3 or 5 ?

Atul Shaw · Accepted Answer

Dear student,Total outcomes when two dices are thrown=36=n(S)Events when sum of two number is less than 10 (A):{(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); (5,1); (5,2); (5,3); (5,4);(6,1); (6,2); (6,3)}n(A)=30Event when sum of two numbers is not divisible by 3 or 5(B):{(1,1); (1,3); (1,6); (2,2); (2,5); (2,6);(3,1); (3,4); (3,5); (4,3); (4,4);  (5,2); (5,3); (5,6); (6,1); (6,2); (6,5)}n(B)=17A∩B:{(1,1); (1,3); (1,6); (2,2); (2,5); (2,6);(3,1); (3,4); (3,5); (4,3); (4,4);  (5,2); (5,3); (6,1); (6,2)}n(A∩B)=15P(A)=n(A)n(S)=3036P(B)=n(B)n(S)=1736P(A∩B)=n(A∩B)n(S)=1536P(A∪B)=P(A)+P(B)+P(A∩B)=3036+1736-1536=3236=89Regards

Two dices were thrown simultaneously . What is the probability that the sum of the two numbers appearing on the top of the dice is less than 10 and is not divisible by 3 or 5 ?