URGENT PROBABILITY HELP

Suppose that in a weekly lottery you have probability .02 of winning a prize
with a single ticket and that you buy 1 ticket per week for 52 weeks.
a. What is the probability that you win no prizes?
b. What is the probability that you win 3 or more prizes?
c. What is the mean and standard deviation of the number of prizes you win

a)
P(not winning per week) = .98
P(0 wins) = (0.98)^52 = .3497

b)
P( 3 or more wins) = 1-P(0 wins)-P(1 win) - P( 2 wins)
P(0 wins) = .3497
P(1 win) = 52C1 (.02)^1 (.98)^51 = 0.3712
P(2 wins) = 52C2 (.02)^2 (.98)^50 = 0.1936

P( 3 or more wins) = 1-P(0 wins)-P(1 win) - P( 2 wins) = 1-.3497-.3712-.1936 =.0855

c)
mean = np =52(.02) =1.04
variance = np(1-p) = 52(.02)(.98) =1.0192
standard deviation = sqrt(1.0192) =1.0096

hi Tiffany -

This is a binomial probability distribution with n = 52 and p = 0.02

a. probability that you win no prizes: P(x = 0) = (1 - 0.02)^52 = 0.3497

b. P(x>=3) = 1 - P(x < 3) = 0.086 , using binomial table on a TI calculator

c. mean = np = 52(.02) 1.04
standard dev = sqrt(52*.02*.98) = 1.01

Hope that helped