A cube with its sides numbered 1— 6 is rolled twice, first landing on

Question

A cube with its sides numbered 1— 6 is rolled twice, first landing on a and then landing on b. If any roll of the cube yields an equal chance of landing on any of the numbers 1 — 6, what is the probability that a + b is prime?

A) 0

B) \(\frac{1}{12}\)

C) \(\frac{5}{12}\)

D) \(\frac{7}{18}\)

E) \(\frac{4}{9}\)

A) 0

B)  \frac{1}{12}

C)  \frac{5}{12}

D)  \frac{7}{18}

E)  \frac{4}{9}

TestPrepUnlimited · Answer

The prime numbers are 2, 3, 5, 7, and 11. Let's not forget there are 6*6 = 36 rolls in total.

2 can be built from 1 + 1 only.
3 = 1 + 2 or 2 + 1. 2 rolls.
5 = 1 + 4 through 4 + 1 which is 4 rolls.
7 = 1 + 6 through 6 + 1 which is 6 rolls.
11 = 5 + 6 or 6 + 5. 2 rolls.

In total that is 1 + 2 + 4 + 6 + 2 = 15 rolls out of 36.  \frac{15}{36} = 5/12 .

Ans: C

BrushMyQuant · Answer

Given that A cube with its sides numbered 1 through 6 is rolled twice, first landing on a and then landing on b. and We need to find If any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6, what is the probability that a + b is prime? 
 
As we are rolling the cube twice => Number of cases =  6^2  = 36

First roll gives a and second roll gives b and we need to find the Probability that a+b is prime => Sum of the two rolls is prime

We know that out of the numbers from 2(1+1) to 12 (6+6) we have only five prime numbers and they are 2, 3, 5, 7 and 11
( Watch this video  if you are not aware of  Prime Numbers )

Following are the possible cases in which sum of the two rolls is a prime number
(1,1), (1,2), (1,4), (1,6)
(2,1), (2,3), (2,5)
(3,2), (3,4)
(4,1), (4,3)
(5,2), (5,6)
(6,1), (6,5)

=> 15 possibilities

=>  Probability that a + b is prime  =  \frac{15}{36}  =  \frac{5}{12}

So,  Answer will be C 
Hope it helps!

Watch the following video to learn How to Solve Dice Rolling Probability Problems

https://www.youtube.com/watch?v=5PVZYQXet18

DanTheGMATMan · Answer

No sweat- just list out the possible prime sums and then list the ways to get there:
 https://www.youtube.com/watch?v=TRCnHz7o9w0

Vitthal19 · Answer

as in the question A and B are 2 different variables given so the case 1,1 should be considered or not?

Krunaal · Answer

a can be equal to b, so (1,1) is possible case.

bumpbot · Answer

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A cube with its sides numbered 1— 6 is rolled twice, first landing on

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A cube with its sides numbered 1— 6 is rolled twice, first landing on

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