Question

Pick one of the following and explain why it’s not quite a binomial experiment (checking the conditions needed to be a binomial experiment)

How would you improve the study to turn it into a binomial experiment?

1. Record the number of different eye colors in a group of 50 randomly selected people.

2. A married couple decide to have children until a girl is born, but to stop at five children if they do not have any girls.

3. A student guesses on every question of a test that has 10 multiple-multiple choice questions and 10 true-false questions. Record the number of questions the student gets right.

Answer 1

1. record the number of different eye colors in a group of 50 randomly selected people - the following data is not a binomial experiment because though every trials are independent but we cannot classify the event as success and failure. We are unable to find the probability of success.

if we record the number of persons having black eye color in a group of people then the experiment is a binomial experiment.

the black eyes people is taken as a success and remaining people as failure.

2. a married couple decided to have a children until a girl is born but stop at five children if they do not have any girl this is not a binomial experiment because there is no concept of success or failure. If we take the total number of girls of a couple or in a family then it is a binomial experiment. We consider born a girl as success and born a boy or others as failure.