Question

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

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?

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.