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  1. #1
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    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?
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  2. #2
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    Re: conditional probability question

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

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

    Quote Originally Posted by anthonye View Post
    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}
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    Re: conditional probability question

    Thank you Plato thats exactly what I needed to know.
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