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Lotto. A previous Arizona state lottery, called Lotto, is played as follows: The player selects six numbers from the numbers 1-42 and buys a ticket for $1. There are six winning numbers, which are selected at random from the numbers 1-42. To win a prize, a Lotto ticket must contain three or more of the winning numbers. A probability distribution for the number of winning numbers for a single ticket is shown in the following table.
Number of
winning numbers
Probability
0
0.3713060
1
0.4311941
2
0.1684352
3
0.0272219
4
0.0018014
5
0.0000412
6
0.0000002
a. If you buy one Lotto ticket, determine the probability that you win a prize. Round your answer to three decimal places.
b. If you buy one Lotto ticket per week for a year, determine the probability that you win a prize at least once in the 52 tries.
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