Question

Two dice are rolled.

A is a event that the sum of the digits on the uppermost faces is at least 10.

B is the event that the sum of the digits on the uppermost faces is 13.

C is the event that the sum of the digits on the uppermost faces is divisible by 5.

D is event that the sum of the digits on the uppermost face is a multiple of 6.

With detailed explanation​

Answer 1

Answer:

Sol. 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

(i) Let A be the event that sum of numbers on their upper faces is divisible by 9

A = { (3, 6), (4, 5), (5, 4), (6, 3) }

n (A) = 4

P (A) = n (A)/n (S)

∴ P (A) = 4/36

∴ P (A) = 1/9

(ii) Let B be the event that sum of number on their upper faces is at the most 3.

B = { (1, 1), (1, 2), (2, 1) }

n (B) = 3

P (B) = n (B)/n (S)

∴ P (B) = 3/36

∴ P (B) = 1/12

(iii)Let C be the event that number on the upper face of the first die is less than the number on the upper face of second die.

C = { (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6) (3, 4), (3, 5), (3, 6), (4, 5), (4, 6), (5, 6) }

n (C) = 15

P (C) = n (C)/n (S)

∴ P (C) = 15/36

∴ P (C) = 5/12