Final answer:
In this lottery, the probability of winning the million-dollar prize with a single ticket, ten tickets, and a ticket that matches 5 numbers is calculated using binomial coefficients.
Step-by-step explanation:
In this lottery, there are 48 balls numbered 1 through 48, and 6 of them are drawn at random without replacement. Let's solve the questions step by step:
a) If the order of the numbers doesn't matter, we need to find the probability of choosing the winning combination of 6 numbers out of 48. The number of ways to choose 6 numbers out of 48 is given by the binomial coefficient C(48, 6) = 48!/(6!(48-6)!). The total number of possible outcomes is given by the number of ways to choose any 6 numbers out of 48, which is C(48, 6). Therefore, the probability of winning the million-dollar prize with a single lottery ticket is 1/C(48, 6).
b) If you purchase 10 tickets, the probability of winning the million-dollar prize with one of the tickets is 10 times the probability calculated in part (a). Therefore, the probability is 10/C(48, 6).
c) If you have a ticket with 5 numbers that exactly match the winning combination, we need to find the probability of choosing the remaining 48-5 = 43 numbers in the correct order. The probability of choosing the correct 43 numbers is 1/C(43, 6). Therefore, the probability of winning in this case is 1/C(43, 6).