Damon rolls three six-sided dice. What is the probability that his tot

Question

Damon rolls three six-sided dice. What is the probability that his total will be greater than 16 ?

A. 1/216
B. 1/108
C. 1/72
D. 1/54
E. 5/216

das.sushmit · Answer

Answer is D.

Probability of an event happening = # of favourable events/ total number of possible events.

Since Damon rolls 3 six-sided dice, total number of possibilities= 6*6*6 = 216 
Events where the sum is greater than 16= (5,6,6) -> 3!/2! = 3 OR (6,6,6) -> 3!/3! = 1 therefore, total is 4.

Probability = 4/216 = 1/54 (D)

Archit3110 · Answer

possible (6,6,6),(6,6,5),(6,5,6),(5,6,6) 
4 options and 3 sided dice so 4/216= 1/54
IMO D

baru · Answer

Total >16 == { (6,6,6) , {5,6,6,}* 3 ways } = Total 4 ways

Prob = 4 / (6*6*6 ) = 4/(36*6) = 1/(9*6) = 1/54 = Option D

BrushMyQuant · Answer

Given that Damon rolls three six-sided dice and we need to find What is the probability that his total will be greater than 16 ?

As we are rolling three six-sided dice => Number of cases =  6^3  = 216

Following are the cases in which the sum will be greater than 16
 5 + 6 + 6  = 17 =>  \frac{3!}{2!}  =  3 cases possible  (3! because we have 3 numbers and 2! because 6 is repeated twice)
 6 + 6 + 6  = 18 =>  1 case

=>  Total cases  = 3 + 1 = 4

=>  Probability that his total will be greater than 16  =  \frac{4}{216}  =  \frac{1}{54}

So,  Answer will be D 
Hope it helps!

Playlist on Solved Problems on Probability  here

Watch the following video to MASTER Dice Rolling Probability Problems

https://www.youtube.com/watch?v=5PVZYQXet18

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Damon rolls three six-sided dice. What is the probability that his tot

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