If a six-sided die with faces numbered one through six is rolled three

Question

If a six-sided die with faces numbered one through six is rolled three times, what is the probability that 5 faces upward for all three rolls?

A. 1/6

B. 1/36

C. 1/96

D. 1/126

E. 1/216

EgmatQuantExpert · Answer

Solution

Given:  
 • A six-sided die with faces numbered one through six is rolled three times

To find:  
 • The probability that 5 faces upward for all three rolls

Approach and Working:  
As six-sided die has all the numbers one through six, the probability of any of the numbers as outcome in one throw is 1/6

• Therefore, the probability that 5 faces upward for all three rolls = 1/6 * 1/6 * 1/6 = 1/216

Hence, the correct answer is option E.

Answer: E

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Archit3110 · Answer

P of getting 5 in a dice in 1 roll = 1/6
so for 3 rolls = (1/6)^3
= 1/216
IMO E

ScottTargetTestPrep · Answer

The probability of rolling a 5 on each roll is 1/6, so the probability of rolling a 5 on each of 3 rolls is 1/6 x 1/6 x 1/6 = 1/216.

Answer: E

BrushMyQuant · Answer

If a six-sided die with faces numbered one through six is rolled three times

As we are rolling a die three times => Number of cases =  6^3  = 216

what is the probability that 5 faces upward for all three rolls?

Only one case out of 216 in which this is possible (5,5,5)

=> P(Getting 5 on all three rolls) =  \frac{1}{216}

So,  Answer will be E 
Hope it helps!

Watch the following video to learn How to Solve Dice Rolling Probability Problems

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

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