Binomial and Hypergeometric Distributions

[Hiche]

Homework Statement

We have an urn with 5 red and 18 blues balls and we pick 4 balls with replacement. We denote the number of red balls in the sample by Y. What is the probability that Y >=3? (Use Binomial Distribution)

Homework Equations

The Attempt at a Solution

Okay, so we were asked to use the Binomial Distribution here.

The whole sample is denoted by N = 23. The number of trials is n = 4 since we have to choose 4 balls from 23. Since Y denotes the number of red balls in the sample and replacement is used, how do we find p? Is it the probability of having 3 red balls and one blues + the probability of 4 red balls? So, (5/23)^3 * (18/23) + (5/23)^4? What is k? Is it in our case 3 and 4?

I will post the other hypergeometric problem when I solve this. I am not good at statistics in any way so I would appreciate the help.

 

[hedipaldi]

Ʃp(y=k},k=3,4
compute p(y=k) from the binomial distribution with probabiliyy 5/18 and n=23

 

[Hiche]

Okay thanks, but shouldn't p = 5/23? The total number of balls is 23.

 

[hedipaldi]

Yes,of course.