Question

Three dice are rolled simultaneously. The probability of getting the total sum of more than $5$ is

• A. $\frac{5}{54}$
• B. $\frac{67}{72}$
• C. $\frac{103}{108}$
• D. $\frac{53}{54}$

Answer 1

The correct option is C $\frac{103}{108}$

Total outcomes=6$\times$6$\times$6=216

For sum to be 3 (1,1,1) is 1

For sum to be 4 (1,1,2),(2,1,1),(1,2,1) is 3

for sum ti be 5 (1,1,3) in 3 ways, (1,2,2) in 3 way total is 6

Total way to get sum less or equal to 5 is 1+3+6=10

Probability that sum less or equal to 5=10/216=5/108

Probability that sum more than 4=1-5/108=103/108