Question

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

An investor randomly purchases 17 stocks listed on a stock exchange.​ Historically, the probability that a stock listed on this exchange will increase in value over the course of a year is 47%.The number of stocks that increase in value is recorded.

Does the probability experiment represent a biniomial​experiment?

A. ​No, because there are more than two mutually exclusive outcomes for each trial.

B. ​No, because the trials of the experiment are not independent.

C. ​Yes, because the experiment satisfies all the criteria for a binomial experiment.

D. ​No, because the probability of success differs from trial to trial.

Answer 1

The experiment in question does satisfy all the criteria for a binomial experiment, including a fixed number of trials, two possible outcomes, and independence of trials, which leads to the answer: Yes, it represents a binomial experiment.

Step-by-step explanation:

The probability experiment described by the student appears to represent a binomial experiment. According to the conditions that define a binomial experiment, we must have the following:

• A fixed number of trials (n).
• Only two possible outcomes for each trial: success or failure.
• The trials are independent of each other and conducted under identical conditions.

In the scenario given, the investor purchases 17 stocks, which is a fixed number of trials (n=17). There are two possible outcomes: the stock increases in value over a year (success) or it does not (failure). The probability of a stock increasing in value is 47%, which defines p (probability of success), and q would be 53% (probability of failure, since q = 1 - p). As long as the stocks are chosen randomly and their performance is independent of each other, the experiment satisfies all the requirements of a binomial experiment.

Therefore, the correct answer to whether this experiment is binomial would be:

C. Yes, because the experiment satisfies all the criteria for a binomial experiment.

Answer 2

Answer:Yes, because the experiment satisfies all the criteria for a binomial experiment.

Step-by-step explanation: The experiment satisfies all the criteria for a binomial experiment because of the following reasons:

(i) There is a fixed number of trial, that is ,binomial experiment deals with either success or failure, yes or no, sweet or bitter, effective or defective etc. So, from the statement , it is either the stock exchange increases or decreases with definitely satisfies the property of binomial experiment . With this point option A can not be answer

`\\`(ii) For binomial experiment, each trial is independent, which means that the rising of the stock exchange is independent of the falling of the stock exchange, with this, option B is also out.

`\\`(iii) The probability of each outcome remain constant from trial to trial. The probability that the stock exchange will increase in value over the course of the year is given to be 0.47, this remain constant throughout the experiment, with this, option D is out