A particular lottery game works by allowing participants to
select three numbers between 0 and 9; the order of the numbers
chosen is also recorded. For instance, 678 and 770 are two possible
selections. Three numbers are then randomly selected. If the
numbers selected match in order the numbers selected by a
participant, that participant wins.
(a) What is the probability that any given participant wins?
(b) A couple of participants are overheard making the following
remarks:
• If I play the lottery 1000 times, then I am guaranteed to win
at least once!
• It is impossible to win the lottery two times in a row.
Discuss how an accurate understanding of probability addresses
these two ideas. Are these participants correct? If not, is there
still some truth in what they are saying?