E-mail and Following Contingency Table
Consider the following contingency table:
What is the probability of
A | B? A′ | B′? A | B′? Are events A and B independent?
4.18
If P(A and B) = 0.4 and P(B) = 0.8, find P(A | B).
½ = 0.5.
4.19
If P(A) = 0.7, P(B) = 0.6, and A and B are independent, find P(A and B).
4.20
If P(A) = 0.3, P(B) = 0.4, and P(A and B) = 0.2, are A and B independent?
Because P(A and B) = 0.20 and P(A)P(B) = 0.12, events A and B are not independent.
Applying the Concepts
4.21
Does it take more time to be removed from an email list than it used to take? A study of 100 large online retailers revealed the following:
Given that three or more clicks are needed to be removed from an email list, what is the probability that this occurred in 2009? Given that the year 2009 is involved, what is the probability that three or more clicks are needed to be removed from an email list? Explain the difference in the results in (a) and (b). Are needing three or more clicks to be removed from an email list and the year independent?
4.22
Do people of different age groups differ in their response to email messages? A survey by the Center for the Digital Future of the University of Southern California (data extracted from A. Mindlin, “Older E-mail Users Favor Fast Replies,” The New York Times, July 14, 2008, p. B3) reported that 70.7% of users over 70 years of age believe that email messages should be answered quickly, as compared to 53.6% of users 12 to 50 years old. Suppose that the survey was based on 1,000 users over 70 years of age and 1,000 users 12 to 50 years old. The following table summarizes the results:
Suppose you know that the respondent is between 12 and 50 years old. What is the probability that he or she answers quickly? 536/1,000 = 0.536. Suppose you know that the respondent is over 70 years old. What is the probability that he or she answers quickly? 707/1,000 = 0.707. Are the two events,
What is the probability of
A | B? A′ | B′? A | B′? Are events A and B independent?
4.18
If P(A and B) = 0.4 and P(B) = 0.8, find P(A | B).
½ = 0.5.
4.19
If P(A) = 0.7, P(B) = 0.6, and A and B are independent, find P(A and B).
4.20
If P(A) = 0.3, P(B) = 0.4, and P(A and B) = 0.2, are A and B independent?
Because P(A and B) = 0.20 and P(A)P(B) = 0.12, events A and B are not independent.
Applying the Concepts
4.21
Does it take more time to be removed from an email list than it used to take? A study of 100 large online retailers revealed the following:
Given that three or more clicks are needed to be removed from an email list, what is the probability that this occurred in 2009? Given that the year 2009 is involved, what is the probability that three or more clicks are needed to be removed from an email list? Explain the difference in the results in (a) and (b). Are needing three or more clicks to be removed from an email list and the year independent?
4.22
Do people of different age groups differ in their response to email messages? A survey by the Center for the Digital Future of the University of Southern California (data extracted from A. Mindlin, “Older E-mail Users Favor Fast Replies,” The New York Times, July 14, 2008, p. B3) reported that 70.7% of users over 70 years of age believe that email messages should be answered quickly, as compared to 53.6% of users 12 to 50 years old. Suppose that the survey was based on 1,000 users over 70 years of age and 1,000 users 12 to 50 years old. The following table summarizes the results:
Suppose you know that the respondent is between 12 and 50 years old. What is the probability that he or she answers quickly? 536/1,000 = 0.536. Suppose you know that the respondent is over 70 years old. What is the probability that he or she answers quickly? 707/1,000 = 0.707. Are the two events,