At a raffle, 1000 tickets are sold at $5 each. There are 20 prizes of $25, 5 prizes of $100, and 1 grand prize of $2000. Suppose you buy one ticket. Let the random variable X represent your net gain...

At a raffle, 1000 tickets are sold at $5 each. There are 20 prizes of $25, 5 prizes of $100, and 1 grand prize of $2000. Suppose you buy one ticket.
Let the random variable X represent your net gain (remember that the net gain should include the cost of the ticket) after playing the game once.

1. Use the table below to help you construct a probability distribution for all of the possible values of X and their probabilities.

X (Net Gain) Probability

1. 
   

   Find the expected value of X, and interpret it in the context of the game.

   
   


2. 
   

   If you play in such a raffle 100 times, what is the expected net gain?

   
   


3. 
   

   What ticket price (rounded to two decimal places) would make it a fair game?

   
   


4. 
   

   Would you choose to play the game? In complete sentences, explain why or why

   
   

   not.

   
   


5. 
   

   If you were organizing a raffle like this, how might you adjust the ticket prices

   
   

   and/or prize amounts in order to make the raffle more tempting while still raising at least $2000 for your organization?