Solve the problem.
-Suppose that there is a lottery that cost $1 to play. You must pick five digits in order from 0 to 9 and duplicates are allowed. If you win, the prize is $7000. What is the expected value of this lottery?
A) -$1.05
B) -$0.98
C) -$0.93
D) -$0.91

Question

Quizplus · Accepted Answer

The total number of possible outcomes when picking five digits from 0 to 9 with duplicates allowed is $10^5 = 100,000$. The probability of winning is $1/100,000$. The expected value (EV) of the lottery can be calculated as follows: EV = (probability of winning * amount won) - (probability of losing * cost to play) = $(1/100,000 * $7000) - ((100,000-1)/100,000 * $1)$ = $$0.07 - $0.99999$ ≈ $-$0.93$.

Solve the Problem. -Suppose That There Is a Lottery That Cost $1 to Cost