A casino is offering a new game where 10 balls (numbered 1 to 10) are placed in a barrel and 3 numbered balls are taken out one at a time. To play the game a player must write 3 numbers in order on a card. If their numbers are drawn out of the barrel in the correct order the player will receive $100. If all their numbers are drawn out but not in the order selected, the player wins $10.
For example suppose a player writes down the numbers 9, 2, and 3. To win first prize the number 9, 2 and 3 must be drawn out in that order. If the numbers 9, 3 and 2 are drawn out in this order then the player receives $10.
(a) How many different ways can the numbers be drawn from the barrel?
(b) What is the probability of winning first prize (i.e. $100)?
(c) What is the probability of wining second prize (i.e. $10)?
(d) Fill in the following probability distribution table and use it to find the expected winnings per game played.
Outcome: First prize
Probability: ?
Winnings: ?
Outcome: Second prize
Probability: ?
Winnings: ?
Outcome: No prize
Probability: ?
Winnings: ?
(e) If the casino wants to make at least 15 cents per game what is the minimum amount they should charge (to the nearest 10 cents).
For example suppose a player writes down the numbers 9, 2, and 3. To win first prize the number 9, 2 and 3 must be drawn out in that order. If the numbers 9, 3 and 2 are drawn out in this order then the player receives $10.
(a) How many different ways can the numbers be drawn from the barrel?
(b) What is the probability of winning first prize (i.e. $100)?
(c) What is the probability of wining second prize (i.e. $10)?
(d) Fill in the following probability distribution table and use it to find the expected winnings per game played.
Outcome: First prize
Probability: ?
Winnings: ?
Outcome: Second prize
Probability: ?
Winnings: ?
Outcome: No prize
Probability: ?
Winnings: ?
(e) If the casino wants to make at least 15 cents per game what is the minimum amount they should charge (to the nearest 10 cents).