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Statistics -Probability or Number of Possibilities Questions

Lotto, a lottery game conducted by the Ohio State Lottery Commission, consisted of selecting six numbers from the 42 numbers 1, 2, ...,41, 42. (No repetitions are allowed, and order does not matter.) The Commission selects by chance the six winning numbers. You pay $1 to play. You get a free ticket if three of your numbers match three of the winning numbers, $75 for matching four numbers, $1500 for matching five numbers, and a large prize if you match all six numbers. The sample space consists of all possible six-number combinations that can be selected. It can be shown that n(S) = 5,245,786. The number of elements in S that match 0, 1, 2, 3, 4, 5, or 6 winning numbers is as follows:

Number of Matches Number of Possibilities
0 1,947,792
1 2,261,952
2 883,575
3 142,800
4 9,450
5 216
6 1

Find the probability of the following:

a. Not winning anything.
b. Getting one or more matches.
c. Winning a free ticket.
d. Getting either $75 or $1500.
e. Winning Lotto Lottery.

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