# Two fair dice (one red and one green) are rolled. What is the probability that the sum is 5, given that the green one is either 4 or 3?

##### 2 Answers

#### Answer:

Probability

#### Explanation:

Let

Let

Then we want

# P( A | B) = (P(A nn B)) / (P(B)) #

Consider first

# P(A nn B) = (n(A nn B)) / (n(T)) #

Where,

And,

If

#G=3 => R=2 #

If#G=4 => R=1 #

And so

# P(A nn B) = 2/36 = 1/18 #

Now, let use calculate

# P(B) = (n(B))/(n(T)) #

Where

If

#G=3 => R=1,2,3,4,5,6 #

If#G=4 => R=1,2,3,4,5,6 #

And so

# P(B) = 12/36 = 1/3 #

And so we can now calculate:

# P( A | B) = (1/18) / (1/3) = 3/18 = 1/6 #

#### Answer:

See other answer for a "proper" discussion of how to evaluate conditional probabilities.

The explanation (below) is simply offered as an alternate, quick-and-dirty way of seeing this result.

#### Explanation:

If green is

and red is

As can be seen from the table:

and

So the probability is