Probability: Another Dice Question: Solving Question

[KevinLuk]

Assume that each die has 6 sides with faces numbered 1 to 6.

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


I'm having a problem with the way it is explained. Thanks.
[spoiler]

The way that I am approaching these questions is that the question is asking for probabilities. The possible outcomes (to me) in which the sums of the dice are over 10 are "5 - 6", "6 - 6", "6 - 6", and "6 - 5". Can somebody please explain to me why the second pair of 6 - 6 is not included in the OA Explanation while "5 - 6" and "6 - 5" are both considered different acceptable probabilities?

Here is the book's explanation:

Solve this problem by calculating the probability that the sum will be higher than 10, and
subtract the result from 1. There are 3 combinations of 2 dice that yield a sum higher than 10: 5 + 6,
6 + 5, and 6 + 6. Therefore, the probability that the sum will be higher than 10 is 3/36, or 1/12. The
probability that the sum will be 10 or lower is 1 - 1/12 = 11/12. [/spoiler]

[DavidG@VeritasPrep]

Can somebody please explain to me why the second pair of 6 - 6 is not included in the OA Explanation while "5 - 6" and "6 - 5" are both considered different acceptable probabilities?

The key is that we're talking about different dice. To conceptualize this, Imagine that the two dice are different colors, one blue and one red. The scenarios that will give us a value over 10 are:

A) Red-5/Blue-6
B) Blue-5/Red-6
C) Red-6/Blue-6

A and B are unique scenarios because we're altering which die is turning up '5' and which is turning up '6.' But clearly, Red-6/Blue-6 would be no different from Blue-6/Red-6.

[Max@Math Revolution]

Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.


Assume that each die has 6 sides with faces numbered 1 to 6.

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


I'm having a problem with the way it is explained. Thanks.

==> the probability that the sum will be smaller than, or will equal 10 = 1 - probability that the sum will be greater than 10

probability = number of cases of a specific event / total number of cases

since two dices have six numbers each, the total number of cases is 6*6=36
the case where the sum is greater than 10 is (5,6),(6,5),(6,6), 3 cases.
therefore the probability that the sum will be smaller than, or will equal 10 = 1-(3C1/36C1)=1-(3/36)=1-(1/12)=11/12



www.mathrevolution.com
l The one-and-only World's First Variable Approach for DS and IVY Approach for PS that allow anyone to easily solve GMAT math questions.

l The easy-to-use solutions. Math skills are totally irrelevant. Forget conventional ways of solving math questions.

l The most effective time management for GMAT math to date allowing you to solve 37 questions with 10 minutes to spare

l Hitting a score of 45 is very easy and points and 49-51 is also doable.

l Unlimited Access to over 120 free video lessons at https://www.mathrevolution.com/gmat/lesson

Our advertising video at https://www.youtube.com/watch?v=R_Fki3_2vO8

[[email protected]]

Hi KevinLuk,

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

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

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

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