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# Three dice are rolled simultaneously. What is the

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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1657 [0], given: 396

Three dice are rolled simultaneously. What is the [#permalink]  08 Dec 2017, 20:37
Expert's post
00:00

Question Stats:

66% (32:50) correct 33% (02:28) wrong based on 3 sessions
Three dice are rolled simultaneously. What is the probability that exactly two of the dice will come up as the same number?

A. $$\frac{5}{12}$$
B. $$\frac{11}{24}$$
C. $$\frac{25}{54}$$
D. $$\frac{13}{27}$$
E. $$\frac{1}{2}$$

Drill 2
Question: 12
Page: 526-527

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Sandy
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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1657 [0], given: 396

Re: Three dice are rolled simultaneously. What is the [#permalink]  29 Dec 2017, 14:12
Expert's post
Explanation

There are a total of 63 = 216 total possible rolls for the three dice.

First figure out the probability of getting exactly two 1’s. There are 5 × 3 = 15 ways this could happen: 112, 113, 114, 115, 116; 121, 131, 141, 151, 161; or 211, 311, 411, 511, 611.

You could repeat this list of 15 possibilities in the obvious way for exactly two 2’s, exactly two 3’s, and so on. Thus, the total number of favorable rolls is 6 × 15 = 90. Because there are 216 possible rolls, 90 of which are favorable, the probability of getting exactly two of the three dice to show the same number is $$\frac{90}{216}=\frac{5}{12}$$, choice A.
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Sandy
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Re: Three dice are rolled simultaneously. What is the   [#permalink] 29 Dec 2017, 14:12
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