Decide whether or not the following experiment is binomial. Explain.

Question

A state lottery randomly chooses six balls, without replacement, numbered 1-40. You choose 6 numbers and purchase a lottery ticket. The random variable x represents the number of matches on your ticket to the numbers drawn in the lottery.

Answer 1

This is the hypergeometric distribrution, not the binomial.

View this as the number of successes in a sample of 6, given 6 successes in a population of size 40.

P(x) = C(6,x)C(34,6-x)/C(40,6) ; alternatively, you can use your calculator/computer's hypergeometric formula. For example, in Excel, you can use =hypgeom.dist(x,6,6,40,0) where x ranges from 0 to 6.

Thus,

P(0) = .3504

P(1) = .4350

P(2) = .1812

P(3) = .0312

P(4) = .0022

P(5) = .000053

P(6) = .000000261

Answer 2

Hello Ariel! I can help you out!

Let's analyze binomial situations must meet the following 4 requirements. The situation must have successes and failures (which is true because if the state lottery picks the number, it succeedes and not is fail), must have probabilities (true) and number of balls n (6), and must be independent. Note that this situation is not independent becuase there are no replacements of the balls done. Therefore, the answer is not binomial. Hope this helped!

Answer 3

Since you are sampling without replacement the individual selection of balls is not independent, so the experiment is not binomial.