What is the probability that the sum of two dice will yield

Question

What is the probability that the sum of two dice will yield a 4 or a 6?

A. 1/9
B. 5/36
C. 7/36
D. 2/9
E. 1/4

My thinking was this...
The # of ways to get a 4: 1 and 3, 2 and 2, 2 and 2, 3 and 1
The # of ways to get a 6: 1 and 5, 2 and 4, 3 and 3, 3 and 3, 4 and 2, 5 and 1
Total of 10
Total possible outcomes = 6 x 6 = 36, therefore the probability is 10/36

This is in the MGMAT book on word translations, page 93. It says the answer is 8/36 because it does not count 2 and 2 and 3 and 3 twice (but it does view 3 and 1 and 1 and 3 as different, likewise it considers 1 and 5 and 5 and 1 different and it considers 2 and 4 and 4 and 2 to be different)

Why does it not count those twice? It is possible to get 2 and 2 two different ways and 3 and 3 two different ways so I thought you needed to account for that.

Bunuel · Accepted Answer

(3, 1) means that you got 3 on the first die and and 1 on the second die, which is different from (1, 3): getting 1 on the first die and and 3 on the second die. Now, (3, 3) means getting 3 on the first die and 3 on the second, which is exactly the same as getting getting 3 on the second die and 3 on the first die.

So, # of favorable outcomes is:
Sum of 4: (1, 3), (3, 1), and (2, 2) --> 3 outcomes;
Sum of 4: (1,5), (5, 1), (2,4), (4, 2), and (3,3) --> 5 outcomes;

Total # of outcomes is 6*6 = 36;

P = (3 + 5)/36 = 8/36 = 2/9.

Answer: D.

Hope it's clear.

Paradox69 · Answer

Perfect explanation, I get it now. Thanks!

BrushMyQuant · Answer

We need to find What is the probability that the sum of two dice will yield a 4 or a 6?

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

Now for the sum to be 4 or 6 we need to find out what comes in both the dice roll. Following outcomes will yield 4 or 6 as the sum
(1,3), (1,5), (2,2), (2,4), (3,1), (3,3), (4,2), (5,1) = 8 outcomes

=> Probability that the sum of two dice will yield a 4 or a 6 =  \frac{8}{36}  =  \frac{2}{9}

So,  Answer will be  \frac{2}{9}  
Hope it helps!

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

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

sspiral2556 · Answer

This question does not feature any answer choices.

Bunuel · Answer

Added the options. Thank you!

dhruva09 · Answer

Short hand trick for two dice questions-

Total events: 6 x 6 = 36

In case of sum of any two numbers of dice, consider the values as n-1 until n=7, and the reverse of those values until n=12. This logic will always remain the same and can be easily visualized.

Sum of two dice = 1 2 3 4 5 6 7 8 9 10 11 12
-------------------------------------------------------------------------------------
Favourable Outcomes= 0 1 2 3 4 5 6 5 4 3 2 1

Favourable Outcomes/Total events
Now, for this question P(4 or 6)= (3+5)/36= 2/9.

What is the probability that the sum of two dice will yield

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What is the probability that the sum of two dice will yield

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