Question

If two dice are rolled simultaneously find the probability of the following events. 1) the sum of the digits on the upper surfaces is atleast 10.2) The sum of the digits on the upper face is33​

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

hope it helps