In a certain game of chance a person pays $5 to play a game. A person randomly selects 2 integers ranging from 0-99. The host of the game then uses a random number generator to select 2 integers ranging from 0-99. If the players values and hosts values agree (in any order), the person playing the game receives $500. Based upon this information, calculate players expected amount of net winnings.

To calculate the player's expected amount of net winnings, we need to determine the probability of winning and losing, as well as the corresponding amounts.

Let's start with the probability of winning. There are a total of 100 possible integers that can be selected by both the player and the host. Since the order doesn't matter for winning, we can calculate the probability using combinations. The player needs to match both integers selected by the host, so the probability of winning is:

P(win) = (2! / (2 - 2)! * (100! / (100 - 2)!) / 100!

Simplifying this expression:

P(win) = (2! / 0!) * (100! / 98!) / 100!

Since 2! / 0! equals 2 and 100! / 98! equals 100 * 99, the expression becomes:

P(win) = 2 * (100 * 99) / 100 * 99 = 2 / 100 = 0.02

So the probability of winning is 0.02 (or 2%).

Next, let's determine the amount the player wins and loses. The player pays $5 to play the game, and if they win, they receive $500. Therefore, the net winnings are calculated by subtracting the cost of playing from the amount won:

Net winnings = Amount won - Cost of playing

Net winnings = $500 - $5 = $495

Now, let's calculate the expected amount of net winnings:

Expected net winnings = P(win) * Net winnings

Expected net winnings = 0.02 * $495 = $9.90

Therefore, the player's expected amount of net winnings in this game is $9.90.