Solution Found!
For the daily lottery game in Illinois, participants
Chapter 5, Problem 66E(choose chapter or problem)
Problem 66E
For the daily lottery game in Illinois, participants select three numbers between 0 and 9. A number cannot be selected more than once, so a winning ticket could be, say, 307 but not 337. 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 (three-digit numbers) are possible?
b. If you purchase a ticket for the game tonight, what is the likelihood you will 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?
Questions & Answers
QUESTION:
Problem 66E
For the daily lottery game in Illinois, participants select three numbers between 0 and 9. A number cannot be selected more than once, so a winning ticket could be, say, 307 but not 337. 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 (three-digit numbers) are possible?
b. If you purchase a ticket for the game tonight, what is the likelihood you will 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?
ANSWER:
Solution 66E
Step1 of 4:
From the given problem we have the participants select three numbers between 0 and 9. And A number cannot be selected more than once, so a winning ticket could be, say, 307 but not 337.
Here our goal is:
a). We need to find the possible number of outcomes.
b). If you purchase a ticket for the game tonight, we need to find the likelihood you will win.
c). Suppose you purchase ‘3’ tickets for tonight’s drawing and select a different number for each ticket. Then, we need to find the probability that you will not win with any of the tickets.
Step2 of 4:
a).
The total number of combinations of three digits with no repeats is then,