What is the probability of rolling three fair dice and having all thre

Question

What is the probability of rolling three fair dice and having all three dice show an odd number?

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

Abhishek009 · Answer

Favourable Outcome = ( ie - 1, 3 , 5 )
Total Outcome = 6 ( ie, 1 , 2 , 3 , 4 , 5 , 6 )

Required Probability =  \frac{3}{6} = \frac{1}{2}

Hence, the Probability of getting an odd number in 3 outcomes is  (\frac{1}{2})^3  =  \frac{1}{8}

Hence, Correct answer will be (B)  \frac{1}{8}

EMPOWERgmatRichC · Answer

Hi All,

We're asked for the probability of rolling three fair 6-sided dice and having all three dice show an ODD number.

The six numbers on a die are 1, 2, 3, 4, 5 and 6 - half of those numbers are odd and half are even.

The probability of rolling an ODD number on each die is 3/6 = 1/2 
The probability of rolling ODD numbers on ALL 3 dice is (1/2)(1/2)(1/2) = 1/8

Final Answer:  B

GMAT assassins aren't born, they're made, 
Rich

BrushMyQuant · Answer

We need to find What is the probability of rolling three fair dice and having all three dice show an odd number?

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

Let's solve the problem using two methods:

Method 1:

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

=>  P(All three are odd)  =  \frac{1}{8}

Method 2:

Out of the 216 comes lets list down the options in which all three outcomes are odd
All three can be odd in 3*3*3 (=27 ways), as in each roll we can get any number out of 1, 3, and 5 => 3 choices in each roll

=>  P(All three are odd)  =  \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 all thre

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What is the probability of rolling three fair dice and having all thre

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