A slot machine has 3 slots. For each slot, the possible outcomes are an apple, orange, lemon, banana, melon, and a joker. When the player puts a coin in the machine, a wheel spins in each of the three slots and stops randomly on one of the possible outcomes. There are different ways to win for each coin played--All 3 jokers are visible, any 3 of a kind that isn't a joker, any 2 jokers, or any 1 joker.

When you play this slot machine, how many possible outcomes are there?

How many ways could you win with 3 jokers?

How many ways could you win with 3 of a kind which were not jokers?

How many ways could you win with 2 jokers?

( Hint: Consider the following: Outcomes of (Joker,Joker, Fruit) + (Joker, Fruit, Joker) + (Fruit, Joker, Joker))

How many ways could you win with 1 joker?

( Hint: Consider the following: Outcomes of (Joker, Fruit, Fruit) + (Fruit, Joker, Fruit) + (Fruit, Fruit, Joker))

Suppose the slot machine pays out the following amounts (after you've put your coin in the machine) for each type of win:

Type of Win Payoff 3 Jokers 30 3 Fruit 10 2 Jokers 4 1 Joker 1 Let X represent your net winnings when you place one coin in the machine. Construct a probability table for the various values of X. (Enter your values of X in numerical order from highest to lowest and use at least 5 decimal places for your probabilities.) Hint: Net Winnings = Payoff -What you paid

Value of X Probability

____ _____

____ _____

____ _____

____ _____

____ _____

On average, how many coins do you expect to win each time you play? (rounded to 4 decimals)

Will you ever actually win/lose this amount?

If you were to play this slot machine 1500 times, how many coins would you expect to win? (rounded to 1 decimal)