A fair coin is tossed four times in a row. What is the probability that the number of heads equals the number of tails?

Equal counts means exactly 2 heads and 2 tails. Total outcomes = $2^4=16$ and the favourable ones number $C(4,2)=6$, so the probability is 6/16 = 3/8. Trap 1/2 argues that heads and tails are equally likely so a tie 'must' happen half the time — in fact a tie is only one of three possible head-counts on either side of the balance. Trap $1/4=C(4,1)/16$ counts exactly one head. Trap 1/16 counts only the single sequence H H T T and ignores the other five orders.