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

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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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

Regards,
Louis

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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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.

Final Answer:

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

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

sum 10 ; 5,6; 6,5 & 6,6
so P ; 3/36
and P <=10 ; 1-3/36 ; 33/36
IMO B

P(<=10) = 1 - P (>10)

= 1 - P ( 11 or 12)

=1 - 3/36

=33/36

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

As we are rolling two dice => Number of cases = \(6^2\) = 36

Now the sum of the two rolls will be between 1+1=2 (when we get 1 on both the dice) and 6+6 = 12 (when we get 6 on both the dice)

So, out of the 36 cases only three cases are there where the sum will be higher than 10. These cases are (5,6), (6,5) and (6,6)
=> Cases with sum as 10 or lower = 36 - 3 = 33

=> Probability that Sum of two dice will yield 10 or lower = \(\frac{33}{36}\)

So, Answer will be B
Hope it helps!

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


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