Question

A fair coin is flipped 20 times. Your friend proposes a bet where if it lands on heads exactly 10 times, you win $4, but if it lands on heads 11 or more times or 9 or less times, you lose $1. Should you take the bet? In other words, find the expected value of the bet and if it is positive you should take it.

Answer 1

E[y]=∑yp(y)=4(0.176)+(−1)(0.824)  =−.12  dollar, so In one play the player is expected to lose 12% of a dollar.