A reception was held for local men and women who own either a large business or
ID: 3257835 • Letter: A
Question
A reception was held for local men and women who own either a large business or a small business. There are 200 people in the room: 50 of the people own a large business, 80 of the people are women, and 90 of the people are men who own a small business.
a.) Prepare a joint frequency table of the data. Make sure the numbers in each cell and the totals in the margins are whole numbers. Label the table appropriately.
b.) Prepare a joint probability table for the data. Be sure to include marginal probabilities.
c.) Suppose that you randomly select one person in the room, what is the probability that the person is a male?
d.) Suppose that you randomly select one person in the room, what is the probability that the person is a female small business owner?
e.) Suppose that you randomly select one person in the room, given that the person owns a large business, what is the probability that the person is a man?
Explanation / Answer
a)
50 people own large business. Therefore the rest 150 people would own small business.
90 of the people are men who own small business. Therefore there would be 60 women who owns small business.
80 of the people are women and 60 of them owns a small business. This means that there would be 20 women who own large business. And hence there will be 30 men who own large business. Since now we have all data we can create the frequency table
b)
To create the joint probability table we will divide all the terms in the frequency distribution table with the total number of people which is 200 in this case.
c)
The probability that a randomly selected person in the room is a male would be 0.60
d)
The probability that a randomly selected person in the room is a female small business owner is 0.30
e)
Given that the randomly selected person owns a large business, the probability of that person being a man would be given by,
P = 0.15/0.25 = 0.60
Small Business Large Business Total Men 90 30 120 Women 60 20 80 Total 150 50 200