Question

In a game you bet $1 and toss two coins. If two heads come up, you win a profit of $75 cents. If two tails come up, no one wins anything. Otherwise, you lose your dollar. What is your expected value of this game?

Answer 1

two heads comes up \(\frac{1}{4}\) of the time

Answer 2

two tails comes up also \(\frac{1}{4}\) of the time, and you get one head and one tail \(\frac{1}{2}\) of the time

Answer 3

expected winning is
\[75\times \frac{1}{4}-1\times \frac{1}{2}\]