Question

A and B throw 3 dice, if A throws a sum of 16 points, the probability of B throwing a higher sum is

• A. $\frac{7}{54}$
• B. $\frac{5}{54}$
• C. $\frac{1}{54}$
• D. $\frac{3}{54}$

Answer 1

The correct option is D $\frac{3}{54}$

A throws 16
B throws more than 16, means B throws, 17 or 18.
Total number of outcomes on throwing 3 dices = $6\times 6\times 6=216$
Favorable outcomes = {(3,6,6), (6,3,6), (6,6,3), (4,6,4), (4,4,6), (6,4,4), (4,5,6), (4,5,6), (5,4,6), (5,6,4), (6,4,5), (6,5,4)}
No. of favorable outcomes = 12
Probability of B throwing a number greater than $16=\frac{12}{216}=\frac{3}{54}$