Final answer:
To give a positive expected value to a player in the big bills game, the minimum chance to win would have to be greater than 2.56%.
Step-by-step explanation:
To calculate the minimum chance to win that would give a positive expected value to a player in the big bills game, we need to consider the cost of entry and the prize amount. In this case, the entry cost is $5 and the prize amount is $200. We can calculate the expected value using the formula:
Expected Value = (Probability of Winning)(Prize Amount) - (Probability of Losing)(Entry Cost)
Let's assume the minimum chance to win is x. Plugging in the given values, we have:
x(200) - (1 - x)(5) > 0
Simplifying the inequality, we get:
195x - 5 > 0
195x > 5
x > 5/195
The minimum chance to win would have to be greater than 5/195, approximately 0.0256 or 2.56%.