Question

Do Generation X and Boomers differ in how they use credit​ cards? A sample of 1000

Generation X and 1000 Boomers revealed the results in the accompanying table.

a. If a respondent selected is a member of Generation​ X, what is the probability that he or she pays the full amount each​ month?

b. If a respondent selected is a​ Boomer, what is the probability that he or she pays the full amount each​ month?

c. Is payment each month independent of​ generation?

PAY FULL AMOUNT EACH MONTH	Generation X	Boomers	Total
Yes	430	590	1020
No	570	410	980
Total	1000	1000	2000

select which of the following for question C.

A. Payment is not independent of generation because the probability of paying in full does not depend on the​ respondent's generation.

B.Payment is independent of generation because the probability of paying in full does not depend on the​ respondent's generation.

C. Payment is independent of generation because the probability of paying in full depends on the​ respondent's generation.

D.Payment is not independent of generation because the probability of paying in full depends on the​ respondent's generation.

Answer 1

The probabilities are calculated by divding the respective respondents by the total of 2000

For example Probability that a selected respondent has paid full amount each month and is member of Generation X = 430 / 2000 = 0.215

Likewise all the other probabilities are calculated and show in the below table

Pay Full amount each month	Generation X	Boomers	Total
Yes	0.215	0.295	0.51
No	0.285	0.205	0.49
Total	0.5	0.5	1

Question (a)

If a respondent selected is a member of Generation​ X, what is the probability that he or she pays the full amount each​ month

Let event B be the respondent selected is a member of Generation​ X

Let event A be the respondent selected pays the full amount each​ month

We need to find P(A | B) which is P(A given B)

P(A | B) = P(A B) / P(B)

= 0.215 / 0.5

= 0.43

If a respondent selected is a member of Generation​ X, what is the probability that he or she pays the full amount each​ month = 0.43

Question (b)

If a respondent selected is a​ Boomer, what is the probability that he or she pays the full amount each​ month?

Let event B be the respondent selected is a Boomer

Let event A be the respondent selected pays the full amount each​ month

We need to find P(A | B) which is P(A given B)

P(A | B) = P(A B) / P(B)

= 0.295 / 0.5

= 0.59

If a respondent selected is a​ Boomer, what is the probability that he or she pays the full amount each​ month = 0.59

Question (c)

Payment is not independent of generation because the probability of paying in full depends on the​ respondent's generation

Here the probabilities of payment each month varies for different generations. so Payment is not independent of generation