In a certain lottery game, you must pick five digits in order from 0 to 9 and duplicates are allowed. If you win, the prize is $10,000. What lottery ticket price would make this game fair?

Question

anonymous · Answer

The number of ways to pick digits is: $$
10^5
$$The number of ways to win is $1$.

It's fair if the expected value is $0$.

$$
E[X] = 0 = 10,000\frac{1}{10^5} + x\frac{10^5-1}{10^5}
$$

anonymous · Answer

Whoops, that formula needs to be changed....

anonymous · Answer

$$
E[X] = 0 = (10,000-x)\frac{1}{10^5} + (-x)\frac{10^5-1}{10^5}
$$

anonymous · Answer

Now you'd solve for $x$.

anonymous · Answer

A
$0.17
B
$0.24
C
$0.08
D
$0.10
???

anonymous · Answer

.10??

anonymous · Answer

Yeah.

anonymous · Answer

Thanks ! :)