A fair game, from a probabilistic standpoint, is one in which the cost of playing the game equals the expected winnings of the game. In other words, if X represents our net winnings (winnings - cost of play), a fair game has E[X] = 0. Suppose we pay $6 to play a game in which 5 tacks are thrown into the air.A tack either lands on its side or its head () with probability 95% and 5% respectively. If no tacks land on their head, we get $0 (i.e. our net winnings is -6 dollars); if exactly one tack lands on its head, we win $10 (i.e. net winnings is $4); if more than one tack lands on its head, we win $20 (i.e. our net winnings is $14).

a) Find the expected net winnings.

b)What would the cost of the game have to be to make this a fair game?Round your answer to two decimal places (i.e. round your answer to the nearest cent)