Question

At Perry's Pumpkin Patch there are 50 pumpkins to choose from in four different colors. Five pumpkins are yellow, 12 are green, 6 are white and the rest are orange pumpkins. Answer the following questions. a) You wl randomly choose 8 pumpkins to take home with you. What is the probability that you have chosen b) c) at least 2 orange pumpkins? What distribution, parameter(s), and support are you using? Given that you have chosen at least 2 orange pumpkins, what is the probability that you have chosen fewer than 5 orange pumpkins? What is the expected value and standard deviation of the number of white pumpkins you have chosen? Over on another field there are 300 pumpkins, 20 of which are white. You are going to randomly choose 10 pumpkins from this larger field. What is the probability that you have chosen at most one white pumpkin d) e) Is there an approximation that can be used on the second field to find the probability that you have chosern at most one white pumpkin? Justify why you can or cannot use an approximation and state its distribution, parameter(s), and support. Find the approximate probability that you have chosen at most one white pumpkin from the second field f)

for (a) hypergeometric or binomial distrbution? im confused, cuz they both look right to me. pls explain the difference.

hypergeoetric: N=50, M=27, n=8

binomial: n=8, p=27/50=0.54

(u dont need to answer those question)

Answer 1

For (a) we need to use Hypergeometric distribution

Because hypergeometric distribution is used in case of sampling without replacement

Whereas Binomial distribution is used in case of with replacement

For binomial distribution probability of success remains constant

Here 8 pumpkins are chosen randomly which means without replacement

So N= 50 , n = 8 , M = 27