Math Is Fun Forum

George92

Guest

Probability question

If anyone could explain how the problem below is done step by step, it would be really appreciated!

Suppose we roll two fair dice.  Find the joint probability mass function of X and Y when X is the largest value obtained and Y is the sum of the values.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Probability question

Well, let’s compute P(X=a,Y=b) (a,b ∈ {1,2,3,4,5,6}).

Clearly b cannot be ≤ a.

If a < b < 2a, then there are two ways of throwing the outcome: a on the first die and b−a on the second, or vice-versa.

If b = 2a, there is only one way: a on both dice.

If b > 2a, then a would not be the maximum of the values of the two dice, so this is not possible. Hence, in summary:

You can also check and satisfy yourself that the sum of all the possible probabilities is 1.

Last edited by JaneFairfax (2007-10-13 14:33:34)