Question

Two dice are thrown. Find the probability of the following events:

Event A : The product of the numbers on their upper faces is 10.

Event B : The sum of the numbers on their upper faces is 10 

Answer 1

Since two dice are thrown,

S ≡ {(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)}

∴ n(S) = 36

(A) Let A ≡ Event of getting the product of the numbers is 10.

A ≡ {(2,5) (5,2)}

∴ n(A) = 2

∴ P(A) = `("n"("A"))/("n"("S")) = 2/36 = 1/18`

∴ P(A) = `1/18`

(B) Let B ≡ Event of getting the sum of the numbers is a multiple of 9.

∴ B ≡ {(3,6) (4,5) (5,4) (6,3)}

∴ n(B) = 4

∴ P(B) = `("n"("B"))/("n"("S")) = 4/36`

∴ P(B) = `1/9`