Hi, this is my first post so hopefully I'm following the proper protocol.
This is not a particularly difficult question, so I'm alarmed that it's stumped me:
If two of the four expressions (x+y), (x+5y), (x-y), and (5x-y) are chosen at random, what is the probability that their product will be of the form (x^2 - (by)^2), where b is an integer?
(A) 1/2 (B) 1/3 (C) 1/4 (D) 1/5 (E) 1/6
I chose C, the right answer is E.
I assumed there was a 1/2 chance of getting an x+y form expression and a 1/2 chance of getting an x-y form expression. The joint chance of getting to independent events should be (1/2)(1/2) = 1/4. But I'm obviously overlooking something.
Thanks for your help.
This is not a particularly difficult question, so I'm alarmed that it's stumped me:
If two of the four expressions (x+y), (x+5y), (x-y), and (5x-y) are chosen at random, what is the probability that their product will be of the form (x^2 - (by)^2), where b is an integer?
(A) 1/2 (B) 1/3 (C) 1/4 (D) 1/5 (E) 1/6
I chose C, the right answer is E.
I assumed there was a 1/2 chance of getting an x+y form expression and a 1/2 chance of getting an x-y form expression. The joint chance of getting to independent events should be (1/2)(1/2) = 1/4. But I'm obviously overlooking something.
Thanks for your help.
