Question

One of the scenarios below is a Binomial Experiment and the other is not. For each​ scenario, state whether or not it is a Binomial Experiment. If it​ is, give the values of n and p and state all the possible values of X. If it is​ not, say why​ (which of the four conditions are not​ met?).

​(a) In the 2008 presidential​ election, 54% of the voters voted for President Obama. Suppose 5 people who voted in the 2008 election are randomly selcted. The random variable represents the number of people in the random sample who voted for President Obama in the 2008 election.

​(b) Suppose that the probability that a randomly selected person who has recently married for the first time will be divorced within 5 years is​ 0.2, and that the probability that a randomly selected person who has recently married for the second time is 0.3. We take a random sample of 20 people who recently married​ (10 for the first time and 10 for the​ second). The sample is chosen so that no one in the sample is married to anyone else in the sample. The

random variable represents the number of people in the sample of 20 who will be divorced within 5 years.

Answer 1

a. Here n is constant, p is same for all, only two outcomes and events are independent

Hence this is binomial distribution with p=0.54 and x=5

X	P(X)
0	0.020596
1	0.120891
2	0.283832
3	0.333194
4	0.19557
5	0.045917

b. Here p is not same for all hence it is not binomial distribution