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# A fair, six-sided die is rolled three times. What is the probability

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Math Expert
Joined: 02 Sep 2009
Posts: 53831
A fair, six-sided die is rolled three times. What is the probability  [#permalink]

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21 Oct 2018, 22:02
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35% (medium)

Question Stats:

57% (01:24) correct 43% (01:49) wrong based on 66 sessions

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A fair, six-sided die is rolled three times. What is the probability that the result of exactly one of the rolls will be an even number?

A. 0.167

B. 0.250

C. 0.333

D. 0.375

E. 0.500

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

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21 Oct 2018, 22:24
Exactly one even in 3 rolls
(Even and odd and odd) or ( odd and even and odd) or ( odd and odd and even)

(1/2*1/2*1/2) *3= 3/8=
0.375

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A fair, six-sided die is rolled three times. What is the probability  [#permalink]

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21 Oct 2018, 22:49
Bunuel wrote:
A fair, six-sided die is rolled three times. What is the probability that the result of exactly one of the rolls will be an even number?

A. 0.167

B. 0.250

C. 0.333

D. 0.375

E. 0.500

A six-sided die has the following features:
1) 2,4, and 6- Even faces
2) 1,3, and 5- Odd faces

We require the probability of exactly one even number of outcome(or face) out of 3 rolls.
The no of outcomes upon rolling a six-sided die 3 times=2*2*2=8=sample space
Exactly one even outcome results in the the following instances:
1) 2-2-2; occurs once
2) 4-4-4; occurs once
3) 6-6-6; occurs once
So, the total no of favorable outcomes=3

So, the required probability=$$\frac{3}{8}=0.375$$
Ans. (D)
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A fair, six-sided die is rolled three times. What is the probability   [#permalink] 21 Oct 2018, 22:49
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