A level probability maths

I have this question and I got part a but I am confused where to start on question b
The probability distribution of a discrete random variable X is given by:

P(X = r) = k(6r2 −r3) for r = 1, 2, 3, 4, 5
P(X = r) = 0 otherwise
(a) Show that k = 1/105
Two values of X are chosen at random.
(b) Find the probability that the product of the two values is even.

Reply 1

mqb2766

Original post by Magicmanzb

You could list (tree/grid) the outcomes/probability of the product of two values and sum the ones that are even. Or do 1-odd probability.

(edited 3 years ago)

Reply 2

Magicmanzb

Original post by mqb2766

You could list (tree/grid) the outcomes/probability of the product of two values and sum the ones that are even. Or do 1-odd probability.

Thank you but how do I work out the values of X?

Reply 3

mqb2766

Original post by Magicmanzb

Thank you but how do I work out the values of X?

If you draw a tree, for instance, you have to consider the different values it can take (as with most probability problems).
If you consider only the pair's that generate even or odd, it cuts down the options a bit.

(edited 3 years ago)

Reply 4

Magicmanzb

Original post by mqb2766

So do I use the numbers 1-5 on the tree?

Reply 5

mqb2766

Original post by Magicmanzb

So do I use the numbers 1-5 on the tree?

Those are the outcomes with a nonzero probability for one score.

A bit of thinking about the question may give an efficient way to get the final probability using even/odd, but failing that, just list the individual probabilities.