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# Two number cubes with six faces numbered with the integers f

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GMAT Club Legend
Joined: 07 Jun 2014
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GRE 1: Q167 V156
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Kudos [?]: 1622 [0], given: 385

Two number cubes with six faces numbered with the integers f [#permalink]  05 Aug 2018, 14:34
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Question Stats:

25% (00:00) correct 75% (00:39) wrong based on 4 sessions
Two number cubes with six faces numbered with the integers from 1 through 6 are tossed. What is the probability that the sum of the exposed faces on the cubes is a prime number?

[Reveal] Spoiler: OA
$$\frac{5}{12}$$

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Sandy
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Intern
Joined: 10 Aug 2018
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Kudos [?]: 12 [0], given: 0

Re: Two number cubes with six faces numbered with the integers f [#permalink]  11 Aug 2018, 12:33
We note which numbers between 1 and 12 are prime numbers (12 is the highest sum two dice can combine for). 2,3,5,7,11.

One combination yields sum 2
Two combinations yield sum 3
Four combinations yield sum 5
Six combinations yield sum 7
Two combinations yield sum 11

So in total 15 combinations yield a prime sum. There are 36 possible ways the dice can land if you roll two dice (6 faces, 2 dice, 6^2=36), and so the probability is 15/36, or 5/12 simplified.
GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4720
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1622 [0], given: 385

Re: Two number cubes with six faces numbered with the integers f [#permalink]  21 Aug 2018, 18:25
Expert's post
Explanation

First think about the prime numbers less than 12, the maximum sum of the numbers on the cube. These primes are 2, 3, 5, 7, 11.

The probability of rolling 2, 3, 5, 7, or 11 is equal to the number of ways to roll any of these sums divided by the total number of possible rolls. The total number of possible cube rolls is 6 × 6 = 36.

Make a list:
Sum of 2 can happen 1 way: 1 + 1.
Sum of 3 can happen 2 ways: 1 + 2 or 2 + 1.
Sum of 5 can happen 4 ways: 1 + 4, 2 + 3, 3 + 2, 4 + 1.
Sum of 7 can happen 6 ways: 1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, 6 + 1.

Sum of 11 can happen 2 ways: 5 + 6, 6 + 5.
That’s a total of 1 + 2 + 4 + 6 + 2 = 15 ways to roll a prime sum.
Thus, the probability is $$\frac{15}{36}=\frac{5}{12}$$.
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Sandy
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Re: Two number cubes with six faces numbered with the integers f   [#permalink] 21 Aug 2018, 18:25
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