Given a weighted coin that lands on heads 55% of the time, you flip the coin until you get you get your first tails. For each heads, you make \$1. When you flip tails you lose \$0.90. What is the expected value of this game?
So far I have come up with the following: Let $X$ be a random variable that takes value 1 with probability 0.55 and -0.90 with probability 0.45. Then $E[X] = 1 \times 0.55 - (0.45 \times 0.90) = 0.145$. I have no idea if this is correct or not though? Would appreciate any help!