Thread: please help

here is a probability question:

if two of the four expressions (x+y), (x+5y), (x-y) and (5x-y) are selected at random, what is the probability of their product being of the form x^2-(by)^2, where b is an integer? thanks in advance

Originally Posted by helpjoe

here is a probability question:

if two of the four expressions (x+y), (x+5y), (x-y) and (5x-y) are selected at random, what is the probability of their product being of the form x^2-(by)^2, where b is an integer? thanks in advance

Probability is not my forte so someone please correct me if I'm wrong.

1.

2.

3.

4.

5.

6.

These are all the different possibilities. Of these only one pair produces the required form, #2. So we need to pick two choices, of which there are only two elements we can choose. So by the counting principle we have 2 choices for the first factor, then we are left with only 1 possibility for the second choice. There are 4*3 ways to make a product of any two of the factors. So:
.

So we have a 1 in 6 chance of getting the required product.

-Dan