A $200 prize is offered in the Big Bills game. One entry costs $5.00. What would the minimum chance to win have to be to give a positive expected value to a player of Big Bills?

greater than 1/5

greater than 1/20

greater than 1/40

greater than 1/10

greater than 1/30

Question

A $200 prize is offered in the Big Bills game. One entry costs $5.00. What would the minimum chance to win have to be to give a positive expected value to a player of Big Bills?

greater than 	1/5


greater than 	1/20


greater than 	1/40


greater than 	1/10


greater than 1/30

kropot72 · Answer

Let p be the probability needed to break even (that is to recover the $5 entry cost. Then we have:
$200 * p = $5
Therefore solving for p gives:
$$p=\frac{5}{200}$$
The chance needed to have a positive outcome must be greater than 5/200, so
$$p>\frac{5}{200}$$
If you simplify the above fraction you will have the correct choice of answer.