please help. Im at a loss for understanding

Question

Bill and Larry toss two coins. If both coins come up heads, Bill pays Larry $5. Larry pays Bill $1 otherwise.

Answer 1

Pr(2H) = (1/2)x(1/2) = 1/4

Pr(not 2H) = 1-1/4 = 3/4

It comes up with equal probability 1/4 for HH, TT, HT and TH

Expected winnings for Larry = (1/4)(5) - (3/4)(1) = 5/4-3/4 = 2/4 = 1/2 = 50 cents. That's an average winning per game. Bill expects to lose, on average 50 cents per game.

If Larry played this coin toss game 10 times, he'd expect to win 10x50 cents =$5

on average, he'd lose 3 times for every 1 time he won. Losing $3 and winning $5 for a net gain of $2 in 4 games.