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

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Math Expert
Joined: 02 Sep 2009
Posts: 58445
A fair, six-sided die is to be rolled 3 times. What is the probability  [#permalink]

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18 Jan 2019, 00:52
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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

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Re: A fair, six-sided die is to be rolled 3 times. What is the probability  [#permalink]

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18 Jan 2019, 07:31
Bunuel wrote:
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

total P of prime ( 2,3,5)
is 3*3*3 - 27
6*6*6 = 216
27/216 = .125
IMO A
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A fair, six-sided die is to be rolled 3 times. What is the probability  [#permalink]

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18 Jan 2019, 07:50
1
Bunuel wrote:
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

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

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Joined: 26 Dec 2018
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Re: A fair, six-sided die is to be rolled 3 times. What is the probability  [#permalink]

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18 Jan 2019, 07:55
Bunuel wrote:
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

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?
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Re: A fair, six-sided die is to be rolled 3 times. What is the probability  [#permalink]

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18 Jan 2019, 08:00
nch2024 wrote:
Bunuel wrote:
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

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?

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.
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Intern
Joined: 26 Dec 2018
Posts: 25
Concentration: Finance, Economics
Re: A fair, six-sided die is to be rolled 3 times. What is the probability  [#permalink]

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18 Jan 2019, 08:12
nch2024 wrote:
Bunuel wrote:
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

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?

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.[/quote]

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.
Re: A fair, six-sided die is to be rolled 3 times. What is the probability   [#permalink] 18 Jan 2019, 08:12
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