In: Statistics and Probability
1- In a large shopping mall, a marketing agency conducted a survey on credit cards. 100 people
were surveyed. The results are shown in the table.
Employment status |
Owns a credit card |
Does not own a credit card |
Total |
Employed |
18 |
26 |
44 |
Unemployed |
25 |
31 |
56 |
Total |
43 |
57 |
100 |
If a person is selected at random, find the following.
a) The probability a person owns a credit card and the person is employed.
b) The probability a person is unemployed or owns a credit card.
c) The odds in favor of a person being unemployed.
d) The odds against a person owning a credit card.
e) The probability a person is unemployed given they own a credit card.
Let, E denotes that a person selected at random, is employed.
Therefore, Ec denotes a person selected at random, is unemployed.
Let, C denotes that a person selected at random owns a credit card.
Therefore, Cc denotes that a person selected at random does not own a credit card.
a) The probability a person owns a credit card and the person is employed, is
b) The probability a person is unemployed or owns a credit card, is
= 0.99 - 0.43 * 0.5814
= 0.74
c) The odds in favor of a person being unemployed, is
d) The odds against a person owning a credit card, is
e) The probability a person is unemployed given they own a credit card, is