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Retired Moderator Joined: 07 Jun 2014
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Two number cubes with six faces numbered with the integers f [#permalink]
Expert's post 00:00

Question Stats: 50% (01:34) correct 50% (10:05) wrong based on 18 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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Re: Two number cubes with six faces numbered with the integers f [#permalink]
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. Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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Kudos [?]: 2971  , given: 394

Re: Two number cubes with six faces numbered with the integers f [#permalink]
2
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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]
In the exam is it necessary that we write fraction in a reduced form ? for e.g For this question can we simply write 15/36 ?
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Re: Two number cubes with six faces numbered with the integers f [#permalink]
Expert's post
No . Absolutely

Ets says" the solution or equivalent fraction"

50/100 = 1/2 Either way is fine

Regards
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GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. Re: Two number cubes with six faces numbered with the integers f   [#permalink] 15 Dec 2019, 09:47
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