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# What is the probability of rolling three fair dice and having none of

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Math Expert
Joined: 02 Sep 2009
Posts: 54496
What is the probability of rolling three fair dice and having none of  [#permalink]

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06 Dec 2016, 11:09
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Difficulty:

15% (low)

Question Stats:

82% (01:04) correct 18% (01:35) wrong based on 110 sessions

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What is the probability of rolling three fair dice and having none of the three dice show a prime number?

A. 5/8
B. 1/8
C. 1/36
D. 1/108
E. 1/216

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Re: What is the probability of rolling three fair dice and having none of  [#permalink]

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07 Dec 2016, 11:14
1
Bunuel wrote:
What is the probability of rolling three fair dice and having none of the three dice show a prime number?

A. 5/8
B. 1/8
C. 1/36
D. 1/108
E. 1/216

There are 3 non prime numbers in a dice - { 1, 4, 6 }
Probability of getting a Non Prime number in a single throw is = $$\frac{3}{6} = \frac{1}{2}$$

So, The probability of getting none of the three dice show a prime number is $$(\frac{1}{2})^3$$

Hence, answer will be (B) $$\frac{1}{8}$$
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Re: What is the probability of rolling three fair dice and having none of  [#permalink]

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03 Aug 2017, 03:18
Probability of non prime nos to appear in 3 rolls
1-P(3 prime nos appear)=1-1/2*1/2*1/2=7/8.
So in that case probability of prime nos not to appear in 3 rolls
=1-7/8=1/8
Option B.
Re: What is the probability of rolling three fair dice and having none of   [#permalink] 03 Aug 2017, 03:18
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