2. (15 points) A new lottery game has the following rules. The cost of each lottery ticket is $10. The player must pick 3 distinct numbers between 1 and 15 located on the ticket and scratch them off. If the three numbers on their ticket match the three numbers drawn by the lottery, they will win $400. If two of the three numbers match, they will win $30 If one of the three numbers match, they will win $15 If no numbers match, they win no money. Let the random variable X = {Net profit to the player} for this lottery game. Give the discrete probability function for this lottery where the random variable X = {Net profit to the player}. Remember when calculating the net profit that there is a $10 cost to play. Give each probability as a fraction (it does not need to be reduced). Do not use decimals. +10) -20 5 a. x P(x) -390 -57 b. Find the expected value, E(X) = , for the game. Round your final answer to the nearest cent. Interpret this number in context of the lottery game. C. If a pla