Suppose that in a weekly lottery you have 2 chance of winnin

Suppose that in a weekly lottery, you have 2% chance of winning a prize with a single ticket. Assume you buy only 1 ticket per week for 52 weeks. What is the probability that you win no prizes? What is the probability that you win 3 or more prizes? What is the mean and standard deviation of the number of prizes you win? What is the probability that the first winning is in the sixth week?

Solution

let X be the number of winning, so X~Bin(52,.02)

a) P(X=0)=(1-0.02)⁵² =.34974856

b) P ( X>2)=1-(P(X=0)+P(x=1) +P( x=2 ))

=1-(0.914066)=0.085934

c) E(X)= 1.04

SD(X)= 1.030157

d) Pwinning at 6th week)=(0.98)* (0.02)⁵