Suppose that after he makes his first shot, he shoots exactly 5 more shots. what is the probability that, out of these 5 attempts, he makes an even number of shots?

The probability of making 2 of 5 shots is 0.31250. The probability of making 4 of 5 shots is 0.15625. So, the probability of making an even number of shots is
.. 0.31250 +0.15625 = 0.46875


p(2 of 5) = (5C2)/2^5 = 10/32
p(4 of 5) = (5C4)/2^5 = 5/32

For the above, we have assumed the probability of success is 1/2.