What is your expected value for a game whose probabilities and outcomes are given in the following table?

Question

%
Profitability Profit
0.2 You win 1.5 times your wager.
0.4 You win your wager.
0.2 You lose 2 times your wager.
0.2 You win nothing.

Answer 1

Ivy, The expected value from a wager should be found by adding each of the individuals probabilities times the amount earned, lost, or not gained. Here, we use the variable "w" for the amount of your wager: E(w)=0.2(1.5w)+0.4(w)+0.2(-2w)+0.2(0) This simplifies to E(w)=0.3w+0.4w-0.4w+0w or E(w)=0.3w. So, if you wagered $1, you'd expect to win 30 cents or $0.30 because E($1)=0.3($1)=$0.3. In the general sense, you'd expect to win 30% of what your wager was.