if the toss of a coin comes down heads, you win two dollars. If it comes down tails, you lose fifty cents. How much would you expect to gain after 25 tosses (in $ dollars)? S

Basically, the probability of heads and tails each is 50% so out of 25 tosses, 12.5 heads and 12.5 tails are expected. Even though, fractional number is not possible still theoretically this is the expected number:

Gain is calculated as follows:

Gain = 12.5 x Gain per toss + 12.5 x Loss per toss

Gain = 12.5 x 2 -12.5 x 0.5

Gain = 18.75