Question

You win $4 if you flip a coin twice and get tails both times. For any other outcome you get nothing. What is the expected value?

Answer 1

expected value in this case is the amount you win times the probability you win it

Answer 2

the probability you get tails both times is
\[\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}\] and
\[\$4\times \frac{1}{4}=\$1\]