Probability Problem Help

[Gbul87]

Hi. I am having trouble with the following problem:
Pick a subset of the integers (1,2,...,100), such that the probability of picking a subset of size k is proportional to k. What is the probability that we pick the subset containing all even numbers?

I got (1/101)* (1/2^99), but the back of the book says (1/2)*(1/2^99). Could someone explain it please?
Thank you!

 

[Steven G]

What does it mean that the probability of picking a subset of size k is proportional to k

 

[Gbul87]

I am not entirely sure... I took as meaning P(K = X) = cX where c is a proportionality constant. Then you would have to calculate the probability of K=50 by solving for c (I got c=1/5050) and multiply that by the probability of getting all 50 even #s (1/2^99). Idk though.