Question

If two dice are rolled simultaneously, find the probability of the following event.
The sum of the digits on the upper faces is at least 10.

Answer 1

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

Event A: 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))`

= `6/36`

= `1/6`

Hence, the probability that the sum of the digits on the upper faces is at least 10 is `1/6`.