What is the probability that the sum of two dice rolls will yield a 4

Question

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

A. 1/9 
 B. 2/9 
 C. 1/3 
 D. 4/9 
 E. 7/9

anwesha1691 · Accepted Answer

We have been asked to find the probability that the sum of 2 dice will yield either 4 or 6.

Two dice thrown makes the total number of cases = 6^2 = 36. 
Favorable cases:
Sum will yield 4 = (1,3), (2,2), (3,1) = 3 cases
Sum will yield 6 = (1,5), (2,4), (3,3), (4,2), (5,1) = 5 cases
Therefore, total favorable cases = 3+5 = 8
Thus, probability that the sum of two dice will yield 4 or 6 = 8/36 = 2/9.

Answer: 2/9

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shrouded1 · Answer

With two dice, enumeration is quite simple

4 = {1 3,2 2, 3 1} = 3 cases
5 = {1 4,2 3,3 2, 4 1} = 4 cases
6 = {1 5,2 4,3 3,4 2,5 1} = 5 cases

So probability is 12/36 or 1/3

One thing you can note for two dice (not really useful in this particular question) is that the most probable outcome is 7. And that the distribution of outcomes is symmetric about 7. So Prob(7+x)=Prob(7-x).

Karastoyanov · Answer

Why did you calculate 5 = {1 4,2 3,3 2, 4 1} = 4 cases? The question asks for 4 OR 6, not from 4 to 6. Please correct me if I'm wrong. Thanks

ScottTargetTestPrep · Answer

There are a total of 6 x 6 = 36 outcomes.

The outcomes that sum to 4 are:

1,3

3,1

2,2

So the probability of getting a sum of 4 is 3/36.

The outcomes that sum to 6 are:

1,5

5,1

2,4

4,2

3,3

So the probability of getting a sum of 6 is 5/36.

Thus, the probability of the dice summing to either 4 or 6 is 3/36 + 5/36 = 8/36 = 2/9.

Bunuel · Answer

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

A. 1/9
B. 2/9
C. 1/3
D. 4/9
E. 7/9

Kinshook · Answer

# of cases with sum yielding 4 = 13, 31, 22 = 3 cases
# of cases with sum yielding 6 = 15, 51, 24, 42, 33 = 5 cases
# of favorable outcomes = 8
# of total outcomes = 6*6 = 36

Probability = 8/36 = 2/9

IMO B

bratbg · Answer

Why does order matter in this case?
I remember solving one similar question in which order was not taken into consideration.

Thanks in advance.

Lampard42 · Answer

Possibilities of Sum 6 and 4 = 33,42,24,15,51 and 22,13,31.
Total Possibilities - 6*6= 36
Probab. = 8/36=2/9 IMO B

Archit3110 · Answer

sum 4; 1,3 ; 2,2 ; 3,1 
sum 6; 1,5 ; 2,4 ; 3,3; 4,2 ; 5,1 
total possiblitiesl 36
and possible pairs; 8
8/36 ; 2/9
IMO B

CareerGeek · Answer

Total outcomes = 36
Favourable for sum 4 = (1,3), (2,2), (3,1) = 3
Favourable for sum 6 = (1,5), (2,4), (3,3), (4,2), (5,1) = 5

Probability of sum 4 OR 6 = 3/36 + 5/36
= 8/36
= 2/9

IMO Option B

Pls Hit kudos if you like the solution

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Vigasimrair · Answer

3/36 + 5/36 = 2/9

Answer B

BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem ↧↧↧

https://www.youtube.com/watch?v=t5SVQHgHZtQ

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

BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem ↧↧↧

https://www.youtube.com/watch?v=t5SVQHgHZtQ

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 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

bumpbot · Answer

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What is the probability that the sum of two dice rolls will yield a 4

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What is the probability that the sum of two dice rolls will yield a 4

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