3.50 Political Affiliation

Question

Political affiliation. 

 

Suppose that in a large population, 51% identify as Democrat. A researcher takes a random sample of 3 people.

1. Use the binomial model to calculate the probability that two of them identify as Democrat.
2. Write out all possible orderings of 3 people, 2 of whom identify as Democrat. Use these scenarios to calculate the same probability from part (a) but using the Addition Rule for disjoint events. Confirm that your answers from parts (a) and (b) match.
3. If we wanted to calculate the probability that a random sample of 8 people will have 3 that identify as Democrat, briefly describe why the approach from part (b) would be more tedious than the approach from part (a).

Answer 1

P(D)=.51

P(2D out of 3) = 3C2(.49)(.51)^2 if you meant probability of exactly 2 out of 3 were Democrats, and not at least 2

= 3!/2!1!(.49)(.51)^2

= 3(.49)(.51)^2

=.382347

= about 38 1/4 % chance

DDR

DRD

RDD

3 ways to get 2 Democrats

divide by total number of possible outcomes if it were P(D)=P(R)=(.50) which is close to P(D)=.51

which also include

DDD

RRR

RRD

RDR

DRR

3 out of 8 = .375 = 37.5% which is slightly less than 38.2%