Question

Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer.

Four cards are selected from a standard​ 52-card deck without replacement. The number of hearts selected is recorded.
Does the probability experiment represent a binomial experiment?
A. No, because the trials of the experiment are not independent and the probability of success differs from trial to trial
B. Yes. because the experiment satisfies all the criteria for a binomial experiment
C. No, because the experiment is not performed a fixed number of times
D. No, because there are more than two mutually exclusive outcomes for each trial

Answer 1

A. No, because the trials of the experiment are not independent and the probability of success differs from trial to trial

Explanation:

A binomial experiment is a statistical experiment that has the following properties:

• The experiment consists of n repeated trials.

• Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure.

• The probability of success, denoted by p, is the same on every trial.

• The trials are independent; that is, the outcome on one trial does not affect the outcome on other trials.

The Case of "four cards are selected from a standard​ 52-card deck without replacement." is not a binomial experiment since

1. probability of success, denoted by p, is not the same on every trial.
2. the outcome on one trial affect the probability of success on other trials