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

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Math Expert
Joined: 02 Sep 2009
Posts: 53063
What is the probability of rolling three fair dice and having all thre  [#permalink]

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06 Dec 2016, 08:33
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Difficulty:

5% (low)

Question Stats:

93% (00:41) correct 7% (01:46) wrong based on 63 sessions

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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

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What is the probability of rolling three fair dice and having all thre  [#permalink]

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06 Dec 2016, 09:48
Bunuel wrote:
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

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) $$\frac{1}{8}$$
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Re: What is the probability of rolling three fair dice and having all thre  [#permalink]

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25 Nov 2017, 14:24
1
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

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Re: What is the probability of rolling three fair dice and having all thre   [#permalink] 25 Nov 2017, 14:24
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