Question

Looking at the Binomial and Hypergeometric situations, list and describe the similarities and differences in the following solutions.

For each of the situations below, answer the following:
Referring to your criteria for selecting a probability distribution, what distribution would be used?
Change the scenario so that the other distribution would be used.  For example, if it is Binomial, change to Hypergeometric.
Scenario 1:

Your manager at work is giving away tickets for the local Lacrosse game.  She has 10 tickets: 4 in the blue section and 6 in the Green section.  She gives you two at random.  What is the probability that they are both in the blue section?

Scenario 2:

40% of the music you listen to is by a Canadian artist.  If you listen to 10 songs, what is the probability that 5 of them are by Canadian artists?

Answer 1

Scenario 1: Here we need to use hyper-geometric distribution since tickets are draw without replacement. The parameters of distribution are

Population size: N = 10

Sample size: n=2

Number of successes in population: n=4

The probability that they are both in the blue section is

Converting to binomial: To convert it in to binomial we need to make draw with replacement.

Scenario 2:

Here binomial distribution with parameters n=10 and p=0.40 will be used. The probability that 5 of them are by Canadian artists is

Converting to hyper-geometric: Assuming 40% songs in the playlist are Canadian artist. To convert it in to hyper geometric distribution we need to select the songs without replacement.