4.121 Winning the Lottery II On Thursday, September 28, 2006, an 85-year-old lady in Etobicoke, Ontario, woke from a dream about winning a lottery, and wrote down the six numbers on a piece of paper. She bought one Lotto 6/49 lottery ticket that day using the numbers 1, 10, 18, 24, 31, and 46. On Friday, she bought another ticket with the same numbers! On Saturday, the real numbers were chosen and her two tickets were both winners. There was one other win- ning ticket sold in another province. The total jackpot was $24,000,000. Because the lady had two of the three winning tickets, she received 2/3 of the jackpot.

a. What is the probability of getting the six correct numbers with one ticket?

b. If two tickets with the same numbers on both tickets are purchased, what is the probability that the pur- chaser would get the correct six numbers?

c. If two tickets with different numbers are purchased, what is the probability of one of the two tickets hav- ing all six winning numbers?

d. Is it a good strategy to select the same numbers twice (if one is only guessing)?

e. If two 6/49 tickets are selected randomly, what is the probability that none of the 12 numbers are repeated?