Three dice are thrown simultaneously. What is the probability that the sum on the three faces is at least 5?

Options

A. `(17)/(18)`
B. `(53)/(54)`
C. `(103)/(108)`
D. `(215)/(216)`

Answer

B

Explanation

As we know that 3 dice are thrown. We want prob. of sum on three faces at least 5 i.e, some may be 5 or more. We will find prob. of sum on three faces not 5 or less. i.e. sum on faces is 3 and 4 (1, 2 is not possible because of 3 dice).
No. of ways for sum on faces not 5 or more =4
[(1,1, 1), (1,2,1), (1, 1, 2). (2, 1, 1)]
Total out comes = 216.
Prob. of not 5 or more= `(4)/(216)`
Prob. of sum on three faces at least 5 `= 1 - (4)/(216) = (212)/(216) = (53)/(54)`.