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.