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Peter rolls two dice at the same time. What is . . .

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Peter rolls two dice at the same time. What is . . .

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Peter rolls two dice at the same time. What is the probability that he will roll a double?

a) 1/12

b) 1/36

c) 1/6

d) 5/12

e) 1/3

The OA is C.

I got confused here. I thought it should be B. Experts, may you explain this PS question to me? Thanks.

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GMAT/MBA Expert

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M7MBA wrote:
Peter rolls two dice at the same time. What is the probability that he will roll a double?

a) 1/12

b) 1/36

c) 1/6

d) 5/12

e) 1/3

The OA is C.

I got confused here. I thought it should be B. Experts, may you explain this PS question to me? Thanks.
You found the probability that Peter would roll two of one particular number. If, for example, we wanted the probability that Peter rolled two 1's, you'd have been right. But he could have rolled two 2's or two 3's, etc.

Put another way, the total number of possible outcomes is 6*6 = 36.
The total number of ways to roll two of the same number would be 6. (two 1's, two 2's, two 3's, two 4's, two 5's, or two 6's.)
Probability of rolling two of the same number = 6/36 = 1/6. The answer is C

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Hi M7MBA,

When the possible outcomes are limited, you might find it beneficial to 'write everything out' - while it would take a little bit of work, you would be able to physically see everything, which would make dealing with the concept easier.

Since we are rolling two 6-sided dice, there are (6)(6) = 36 possible outcomes. Those outcomes are....

11,12,13,14,15,16
21,22,23,24,25,26
31,32,33,34,35,36
41,42,43,44,45,46
51,52,53,54,55,56
61,62,63,65,65,66

There are 6 'pairs' of numbers (11, 22, 33, 44, 55, 66), so the answer to the question is 6/36 = 1/6

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

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GMAT/MBA Expert

Post
Quote:
Peter rolls two dice at the same time. What is the probability that he will roll a double?

a) 1/12

b) 1/36

c) 1/6

d) 5/12

e) 1/3

The OA is C.

I got confused here. I thought it should be B. Experts, may you explain this PS question to me? Thanks.
Hi M7MBA,
Let's take a look at your question.

Peter rolls two dice at a time, so let's first find the total number of outcomes.

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

All possible outcomes when two dice are rolled at the same time = 36
We are asked to find the probability that he will roll a double.

The outcomes for rolling a double will be:
(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)

Total outcomes for rolling a double = 6

Probability of rolling a double = (Total outcomes for rolling a double) / (All possible outcomes when two dice are rolled)
Probability of rolling a double = 6/36 = 1/6

Therefore, Option C is correct.

Hope it helps.
I am available, if you'd like any follow up.

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Post
M7MBA wrote:
Peter rolls two dice at the same time. What is the probability that he will roll a double?

a) 1/12

b) 1/36

c) 1/6

d) 5/12

e) 1/3
Notice that the probability doesn't change if we roll one die first and the other die second. So, let's do this.

Let die #1 the first die, and let die #2 be the second dice

P(both dice are the same) = P(die #1 is any value AND die #2 matches die #1)
= P(die #1 is any value) x P(die #2 matches die #1)
= 1 x 1/6
= 1/6
= C

ASIDE: Some people might wonder how I found the first probability to equal 1.
We need to recognize that the first die can be any value and, in order to get a double, the second guy must match the first die.
Once we have rolled the first die, there is a probability of 1/6 that the second die matches the first die.


Cheers,
Brent

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