Question

A market research company surveyed consumers to determine their ranked preferences of energy drinks among the brands Monster, Red Bull, and Rockstar.
a. What are the outcomes of this experiment for one respondent?

b. What is the probability that one respondent will rank Red Bull first?

c. What is the probability that two respondents will both rank Red Bull first?

Answer 1

Answer with explanation:

Given : The number of energy drink's brands = Monster, Red Bull, and Rockstar.

a. The  possible outcomes of this experiment for one respondent :-

{(Red bull, Monster , Rockstar),(Red bull, Rockstar, Monster ),(Monster, Red Bull, and Rockstar), (Monster, Rockstar, Red Bull), (Rockstar, Monster, Red Bull), (Rockstar , Red Bull, Monster)}

b. Total number of outcomes = 6

Number of outcomes where Red Bull ranked first =2

The  probability that one respondent will rank Red Bull first will be :-

$=\dfrac{2}{6}=\dfrac{1}{3}$

c.  Since each respondent is independent of each other.

The probability that two respondents will both rank Red Bull first will be :-

$(\dfrac{1}{3})^2=\dfrac{1}{9}$