A fair, six-sided die is to be rolled 3 times. What is the probability

Question

A fair, six-sided die is to be rolled 3 times. What is the probability that the die will land on a prime number each time?

A 0.125
B 0.25
C 0.5
D 0.75
E 0.9

Archit3110 · Answer

total P of prime ( 2,3,5)
is 3*3*3 - 27
6*6*6 = 216
27/216 = .125
IMO A

KanishkM · Answer

Probability = Favorable Outcomes / Total outcomes

Total outcomes =  6^3 , Since a dice has 6 sides

Favorable outcomes =  3^3 , Since each dice will have 3 prime numbers 2,3 and 5

Probability = 3^3 / 6^3
= 1/8 
=0.125

Answer A

nch2024 · Answer

I concluded that the answer was A because there are 3 prime numbers on a 6-sided die (2,3,5), which makes the probability of rolling a prime number 1/2. The probability of rolling a prime numbers on 3 consecutive rolls is 1/2*1/2*1/2=1/8 or .125.

However, I was a bit skeptical of my answer due to the wording "will land on a prime number each time?" The phrase "each time" lead me to believe the question may be asking for the individual probability of each roll, which would lead the reader to conclude the answer to be C. Can anyone provide further clarity?

KanishkM · Answer

IMO, in the question it has mentioned the player will throw the die 3 times, automatically the sample space from 6 became 216.

If it would have not mentioned  3 times , then we could have concluded the answer as 1/2 which is 3/6( 3 prime numbers out of 6 total numbers)

Let me know if this helps in some way.

nch2024 · Answer

IMO, in the question it has mentioned the player will throw the die 3 times, automatically the sample space from 6 became 216.

If it would have not mentioned  3 times , then we could have concluded the answer as 1/2 which is 3/6( 3 prime numbers out of 6 total numbers)

Let me know if this helps in some way.

Yes, that helps! As you mentioned, I believe the mention of 3 dice rolls allows us to conclude that we are searching for the probability of prime number on  EACH OF THE 3 ROLLS .

AmarpreetK · Answer

We need to find a shortest and most intuitive way of answering question in GMAT.
Since probability = No of Desirable Outcomes / Total Outcomes.
Each dice having 6 sides when rolled thrice will have 6*6*6 total outcomes.
Desirable outcomes = No of Desirable prime no (2,3,5)
Probability = 3/6 * 3/6 * 3/6 = 1/8 = 0.125
The Correct Answer is A

BrushMyQuant · Answer

Given that a fair 6-sided die is rolled three times and We need to find What is the probability that the die will land on a prime number each time?

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

In each toss we need to get a prime number => For each toss there are 3 favorable outcomes out of 6. (Getting a 2, 3, 5)

=> Probability of getting a prime number in one toss =  \frac{3}{6}  =  \frac{1}{2}

=> Probability of getting a prime number in any of the three tosses =  \frac{1}{2}  *  \frac{1}{2}  *  \frac{1}{2}  =  \frac{1}{8}  = 0.125

So,  Answer will be A 
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

A fair, six-sided die is to be rolled 3 times. What is the probability

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