Question

two dice are rolled simultaneously.
The sum of the digits on upper faces is a multiple of 6
Event B: The sum of the digits on the upper faces is minimum 10.
yent C: The same digit on both the upper faces.​

Answer 1

Answer:

Sample space, 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 the sum of the digits on the upper faces is at least 10. ∴ A = {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)} ∴ n(A) = 6 ∴ P(A) = n(A)n(S)n(A)n(S) = 6/36 ∴ P(A) = 1/6 ii. Let B be the event that the sum of the digits on the upper faces is 33. The sum of the digits on the upper faces can be maximum 12. ∴ Event B is an impossible event. ∴ B = { } ∴ n(B) = 0 ∴ P(B) = n(B)n(S)n(B)n(S)= 0/36 ∴ P(B) = 0 iii. Let C be the event that the digit on the first die is greater than the digit on the second die. C = {(2, 1), (3, 1), (3,2), (4,1), (4,2), (4, 3), (5, 1), (5,2), (5,3), (5,4), (6,1), (6,2), (6, 3), (6, 4), (6, 5), ∴ n(C) = 15 ∴ P(C) = n(C)n(S)n(C)n(S)= 15/36 ∴ P(C) = 5/12 ∴ P(A) = 1/6 ; P(B) = 0; P(C) = 5/12Read more on Sarthaks.com - https://www.sarthaks.com/847469/dice-rolled-simultaneously-find-probability-following-events-digits-upper-faces-least