Determine whether the following probability experiment a bin

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

An investor randomly purchases 16 stocks listed on the stock exchange. Historically, the probability that a stock listed on this exchange will increase in value over the course of the year is 40%. The number of stocks that increase in value is recorded.

Does the probability experiment represent a binomial experiment.

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

b. No because the trials of the experiment are not independent.

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

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

Solution

For an experiment to be called a binomial experiment, it has to satisfy thefollowing four conditions.

1) Fixed number of trails (In this case, 16 stocks)

2) Each trial has only two possible outcomes ( one possible outcome is that the stock value is increased and the other is that the stock value is decreased)

3) each trial is indipendent of the others (yes, each stack has 40% chance to increase in value)

4) probability of the outcomes remains the same from trail to trial (all stocks have 40% chance to increase in value)

since the probability experiment satisfies all the conditions of binomial experiment, the answer is

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