Question

In a giveaway raffle for several prizes, probability of obtaining a winning ticket in any of the attempts is 1/20 with the names replaced in the box every time.

a) What is the probability of winning two prizes by the 14^th draw?

b) What is the probability of winning a prize by the 9^th draw?

c) Identify each probability distribution by its name?

Answer 1

Let X be random variable of number of drawn for kth times wining

X~Negative binomial (k ,p)

pmf of X is

# a)

here k=2 and p=1/20

probability that winning two prizes by 14th draw

-------------------------------ans

# b) probability that winning a prize by 9th draw

here k=1 and p=1/20

P(X=9)=0.25667----------------------------------------ans

# first probability distribution is negative binomial with k=2 ;p=1/20

# second probability distribution is negative binomial with k=1 ;p=1/20 ; also called geometric distribution