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

Question

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

Abhishek009 · Answer

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}

FB2017 · Answer

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.

BrushMyQuant · Answer

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

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

We know that between 1 to 6 there are three prime numbers 2, 3 and 5
=> Prime numbers are 3 out of 5 and non-prime or composite numbers are also 3 out of 6

Let's solve the problem using two methods:

Method 1:

Now there are 8 outcomes possible
(Prime, Prime, Prime), (Prime, Prime, Composite), (Prime, Composite Prime), (Prime, Composite, Composite), (Composite, Prime, Prime), (Composite, Prime, Composite), (Composite, Composite Prime), (Composite, Composite, Composite) and there is an equal chance of each of them happening

=>  P(None is Prime = All Composite)  =  \frac{1}{8}

Method 2:

Now, none of the three dice should show a prime number
=> Each dice has three choices (1, 4, 6) to pick from
=> We will have 3 * 3 * 3 = 27 such cases

=>  Probability that none of the three dice show a prime number  =  \frac{27}{216}  =  \frac{1}{8}

So,  Answer will be B 
Hope it helps!

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

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

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

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