please answer only PART C

In a common type of lottery, a customer buys a ticket with a three-digit number from 000 to 999. A machine (such as one with bouncing balls numbered 0 to 9) then selects a number in this range at random. Each ticket bought by a customer costs $2, whether the customer wins or loses. Customers with winning tickets are paid $900 for each winning ticket. Complete parts (a) through (c) below. (a) Construct a probability distribution of the random variable X that denotes the net amount won by a customer. (Notice that each customer pays $2 regardless of whether he or she wins or loses.) X M") - 2 0.999 898 0.001 (Simplify your answers.) (b) Is this a fair game? (A game involving chance is said to be a fair game if the expected amount won or lost is zero.) Does the state want a fair game? This is not a fair game because E(X) = -1.1 dollar(s). The state wants a game such that E(X) is less than $0, so it does not want a fair game. (Simplify your answer.) (c) Interpret the expected value of X for a person who plays the lottery. Select the correct choice below and, if necessary, ll in the answer box to complete your choice. (Simplify your answer.) 0 A- In the long run, the person will prot. On average, the person will gain $D for every ticket bought. 0 B. In the long run, no one will prot. On average, the person will break even when playing this lottery. O C- In the long run, the state will prot. On average, buying a ticket in the lottery is like paying the state $ O D- In the long run, the person will prot. On average, the person will win $ for every ticket bought