Two dice are rolled. What is the probability the sum will be greater

Question

Two dice are rolled. What is the probability the sum will be greater than 10?

A. 1/9.
B. 1/12.
C. 5/36.
D. 1/6.
E. 1/5.

14101992 · Answer

Combinations possible: (6,6) , (5,6) , (6,5) = 3
Total combinations possible: 6*6=36

Answer = 3/36 = 1/12  Option B.

saicharan1191 · Answer

Possible combinations (5,6) (6,5) (6,6) prob = 3/36 =1/12

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MartyTargetTestPrep · Answer

Total Number of Possibilities First Die: 6

Total Number of Possibilities Second Die: 6

Total Number of Possibilities Two Dice Together: 6 x 6 = 36

Dice have numbers 1 to 6.

Highest Possible Sum Using 1: 1 + 6 = 7

Highest Possible Sum Using 2: 2 + 6 = 8

Highest Possible Sum Using 3: 3 + 6 = 9

Highest Possible Sum Using 4: 4 + 6 = 10

If one of the dice shows 1 to 4, the sum will not be greater than 10.

Also, 5 + 5 = 10.

So, there are only three combinations that add up to sums greater than 10.

5 + 6 = 11

6 + 5 = 11

6 + 6 = 12

(Combinations That Add Up to Sums Greater Than 10)/(Total Combinations) = 3/36 = 1/12

The correct answer is (B).

Loser94 · Answer

Total Outcomes = 6*6 =36
Fav Outcome= 6,4 6,5 6,6 only 3 cases which give sum greater than 10 so 
Prob :3/3 =1/12
Answer B

ScottTargetTestPrep · Answer

The rolls that will allow for a sum greater than 10 are:

(6,5) or (5,6) or (6,6)

Since there are a total of 6 x 6 = 36 outcomes, then the probability that the sum will be greater than 10 is 3/36 = 1/12.

Answer: B

tottendulkar · Answer

Why aren't we considering (6,6) twice?

Just the way (5,6) and (6,5) were considered as per "5 on the first dice and 6 on the 2nd dice and vice-versa", why shouldn't we consider 2 possibilities of (6,6) the same way?

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Kritisood · Answer

Quoting an egmat quant experts response to this:

When two dice are rolled, we get a total of 36 outcomes. All the the possible outcomes are:

(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)

You can see in the above outcomes (5,6), (6,5), (6,6) are different possible outcomes of dices and occur only once. So when we are taking (6,5) & (5,6) we are essentially taking two different outcomes and not taking the outcomes twofold. Similarly (6,6) is a different outcome and if we take (6,6) outcome twofold it will be repetition of the outcome already taken.

serenayong · Answer

but if the dices are technically the "SAME" (eg. same color, size etc), (5,6) = (6,5), no?

BrushMyQuant · Answer

Given that Two dice are rolled and we need to find What is the probability the sum will be greater than 10?

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

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)

=> Probability that the sum will be greater than 10 =  \frac{3}{36}  =  \frac{1}{12}

So,  Answer will be B 
Hope it helps!

Playlist on Solved Problems on Probability  here

Watch the following video to MASTER Dice Rolling Probability Problems

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

Gijmaja · Answer

There are only 3 options out of 36 => 3/36=1/12

Two dice are rolled. What is the probability the sum will be greater

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Two dice are rolled. What is the probability the sum will be greater

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