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What is the probability that the sum of two dice will yield a 10 or lo

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What is the probability that the sum of two dice will yield a 10 or lo  [#permalink]

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New post Updated on: 11 Nov 2017, 00:22
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What is the probability that the sum of two dice will yield a 10 or lower?

A. 34/36
B. 33/36
C. 32/36
D. 31/36
E. 30/36

Its the question from Manhattan GMAT Number Proporties page 65.

Im not able to to understand ehy there are just three combination (5+6,6+5,6+6) and not 4 with the 6+6 again??

I´m such an idiot :)

Originally posted by Henni on 10 Nov 2017, 15:00.
Last edited by Bunuel on 11 Nov 2017, 00:22, edited 1 time in total.
Renamed the topic and edited the question.
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Re: What is the probability that the sum of two dice will yield a 10 or lo  [#permalink]

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New post 10 Nov 2017, 16:19
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Henni wrote:
Its the question from Manhattan GMAT Nzmber Proporties page 65.

What is the probability that the sum of two dice will yield a 10 or lower?

Im not able to to understand ehy there are just three combination (5+6,6+5,6+6) and not 4 with the 6+6 again??

I´m such an idiot :)

Dear Henni,

I'm happy to respond. :-)

My friend, think of physical dice. To make it easy to distinguish them, let's say we have one red die and one green die. What are the possibilities in which the sum is greater than 10?
(1) red = 5, green = 6
(2) red = 6, green = 5
(3) red = 6, green = 6

There's only one way to get 12--that's when both the red die and the green die show a 6. There's only one way for that to happen, whereas in the case of 11, there are two different things each die is doing to get those two results.

Does this make sense?
Mike :-)
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Re: What is the probability that the sum of two dice will yield a 10 or lo  [#permalink]

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New post 15 Jan 2018, 06:40
Dear all,

Just in case someone does not prefer to find the probability of the sum greater than 10, and then subtract the answer from 1 to get the probability of the sum a 10 or below, see below:

All possibilities of the sum a 10 or below:

Die 1 (value) | Die 2 (no of possibilities)
1 | 6 cases (1 to 6)
2 | 6 cases (1 to 6)
3 | 6 cases (1 to 6)
4 | 6 cases (1 to 6)
5 | 5 cases (1 to 6)
6 | 4 cases (1 to 6)
Total = 33 cases

All possibilities for 2 dies = 6 x 6 = 36 cases

Probability of sum a 10 or below = 33/36

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Re: What is the probability that the sum of two dice will yield a 10 or lo  [#permalink]

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New post 15 Jan 2018, 07:11
Henni wrote:
What is the probability that the sum of two dice will yield a 10 or lower?

A. 34/36
B. 33/36
C. 32/36
D. 31/36
E. 30/36

Its the question from Manhattan GMAT Number Proporties page 65.

Im not able to to understand ehy there are just three combination (5+6,6+5,6+6) and not 4 with the 6+6 again??

I´m such an idiot :)


There are 3 possible combination for to get higher than 10 from two dices:

D1 - 6 + D2- 6 = 12
D1 - 6 + D2- 5 = 11
D1 - 5 + D2- 6 = 11

Now total combinations = 6*6 = 36
Remaining combinations = 36 - 3 = 33

Hence, probability to get 10 or lower = 33/36.
Answer B.
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Re: What is the probability that the sum of two dice will yield a 10 or lo  [#permalink]

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New post 17 Feb 2018, 13:43
Hi All,

With this prompt, 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 all of the possibilities, 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
61,62,63,64,65,66

Of these 36 outcomes you can either calculate what you WANT or what you DON'T WANT (and subtract that from the number 1). The second method is easier here...

There are 3 options that DO NOT fit what you're looking for.... 3/36 = 1/12

1 - 1/12 = = 11/12 = the options that you ARE looking for.

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Re: What is the probability that the sum of two dice will yield a 10 or lo  [#permalink]

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New post 18 Feb 2018, 00:31
Try to first figure out is calculating the favorable probability easy or calculating the non-favorable probability is easy.Here calculating the non favorable probability would be easy.So non favorable event would be getting a 11 or 12.

Probability of getting a 11 is Favorable outcomes/Total Outcomes=2/36.
Probability of getting a 12 is 1/36
So required probability=1-(1/36+2/36)
=1-3/36=33/36
So answer is B
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Re: What is the probability that the sum of two dice will yield a 10 or lo &nbs [#permalink] 18 Feb 2018, 00:31
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