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

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Re: What is probability that the sum of two dice will yield 4 or 6? [#permalink]
shrouded1 wrote:
prashantbacchewar wrote:
What is probablity that the sum of two dice will yield 4 ot 6

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).

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
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Re: What is probability that the sum of two dice will yield 4 or 6? [#permalink]
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prashantbacchewar wrote:
What is probability that the sum of two dice will yield 4 or 6?

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.
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What is probability that the sum of two dice will yield 4 or 6? [#permalink]
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↧↧↧ Detailed Video Solution to the Problem ↧↧↧

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

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What is probability that the sum of two dice will yield 4 or 6? [#permalink]
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