Question

Sophia has four tickets to a concert. Six of her friends, Yolanda, Michael,

Kevin, Marissa, Annie, and Katie, have all expressed an interest in going to
the concert. Sophia decides to randomly select three of her six friends to
attend the concert.
a) List all possible samples of size n = 3 from the population of size N = 6.
Once an individual is chosen, he or she cannot be chosen again.
b) Comment on the likelihood of the sample containing Michael, Kevin, and
Marissa

Answer 1

Step-by-step explanation:

a) There are 20 possibilities

Let us consider the initials of her friends to make the solution easier- Yolanda (Y), Michael (M), Kevin (K), Marissa (Ma), Annie (A), Katie (Ka)

Let's make a sample space of size n=3, where a person cannot be chosen more than once

YMK, YMMa, YMA, YMKa, YKMa, YKA, YKKa, YMaA, YMaKa, YAKa, MKMa, MKA, MKKa, MMaA, MMaKa, MAK, KMaA, KMaKa, KAKa, MaAKa

b) The likelihood of the sample containing Michael , Kevin and Marissa is (MKMa) is 1/20 or 5%.

We can see from the sample space above that the sample MKMa is only written once. To find the likelihood-

To number of desired samples present/ Total sample space

Therefore, 1/20

To convert this into a percentage we will multiply by 100,

1/20 x 100 = 5%