# Math Help - conditional probability question

1. ## conditional probability question

Hi;
the question is two dice are thrown and there product is recorded,
given that one die lands on a 2 find the probability of the dice is exactly 6?

I get 1/6 = 0.1667 the reason I get this is because the other dice needs to land on a 3.

is this correct?

2. ## Re: conditional probability question

assuming the question is 'find the probability that the product of the dice is exactly 6' then yes correct

3. ## Re: conditional probability question

If you wanted to show it formally (not necessary however)

Let A and B be events with A = "The first die is 2" and B = "The product of the dice is 6", then

$P(B|A) = \frac{P(A and B)}{P(B)}$

As you said, the other dice needs to be a 3 and hence $P(A and B) = \frac{1}{36}$ and $P(B) = \frac{1}{6}$ and hence $P(B|A) = \frac{1}{6}$

4. ## Re: conditional probability question

Thank you;
Does the probability stay the same if its the second dice that shows a 2?

5. ## Re: conditional probability question

Originally Posted by anthonye
the question is two dice are thrown and there product is recorded, given that one die lands on a 2 find the probability of the dice is exactly 6?

Perhaps I have misread the question. Is it, "find the probability that the product of the dice is exactly 6, given that one die lands on a 2"?

If that is indeed the question then the answer is $\frac{2}{11}$.
Thinking in terms of pairs, there are eleven pair that contain a two. Of those, only two pair also contain a three.

If $A$ is the event that the product is six and $B$ is the event that one die lands on a 2, then
$\mathcal{P}(A|B)=\frac{\mathcal{P}(A\cap B)}{\mathcal{P}(B)}=\frac{2/36}{11/36}=\frac{2}{11}$

6. ## Re: conditional probability question

Thank you Plato thats exactly what I needed to know.