Question

Three six faced fair dice are rolled together. The probability that the sum of the numbers appearing on the dice is 8, is

• A. $\frac{7}{72}$
• B. $\frac{7}{54}$
• C. $\frac{4}{27}$
• D. $\frac{7}{64}$

Answer 1

The correct option is A $\frac{7}{72}$

Getting sum 8 when three dice are rolled = E
The possibilities are (1,1,6) , (2,2,4), (3,3,2), (1,2,5), (1,3,4)
The number of favorable cases for E = 3 + 3 + 3 + 6 + 6 = 21
The total number of cases = $6^3$ = 216
Required probability P(E) $=\frac{21}{216}=\frac{7}{72}.$