4 For the daily lottery game in a particular state participa

4. For the daily lottery game in a particular state, participants select four numbers between 0 and 9. A number cannot be selected more than once, so a winning ticket could be 3071 but not 3371. The order of selection is important. Purchasing one ticket allows you to select one set of numbers. The winning numbers are announced on TV each night. a. How many different outcomes (four-digit numbers) are possible? b. If you purchase a ticket for the game tonight, what is the probability that you win? c. Suppose you purchase three tickets for tonight?s drawing and select a different number for each ticket. What is the probability that you will not win with any of the tickets?

Solution

There are 4 slots that are to be filled

_ _ _ _ . HOwever, the first slot can\'t be zero and hence can be filled in oly 9 ways.

The next blank can be filled with a zero or 8 other ways.

Thus, total number of ways = 9 * 9 * 8 * 7 = 4536 ways

b) Chance of winning on one lottery = 1 / 4536

which is the required probability for part B

c)

P (Winning) = 3 * (1 / 4536)

= 1 / 1512

P (Not winning) = 1 - 1/1512

= 1511 / 1512

Hope this helps.Ask if you have any doubts.