A previous state lottery is played as follows: The player selects six numbers fr

Question

A previous state lottery is played as follows:
The player selects six numbers from the numbers 1-42 and buys a ticket for $1.
There are 6 winning numbers, which are selected at random from numbers 1-42.
To win the prize, a lotto ticket must contain 3 or more of the winning numbers.
A probablity distrubution for a winning ticket is show below:
# of winning tickets/probablity
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 1 lottery ticket, detrmine the probablity that you win a prize. Round answer to 3 decimal places.

b. If you buy one lotto ticket per week for a year, determine the probabilty taht you win a prize at least once in the 52 tries.

Explanation / Answer

N follows binomial distribution with n = 52 and p = 0.029 (found in a) P(N >= 1) = 1 - P(N=0) = 1 - 0.2165 = 0.7835

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