The table shows the results of a survey in which 28,295 adults were asked whethe
ID: 3151229 • Letter: T
Question
The table shows the results of a survey in which 28,295 adults were asked whether they had a cold or the flu on the previous day.
Colds
Flu
Neither
Total
Smoker
526
153
4,980
5,659
Nonsmoker
1,494
430
20,712
22,636
Total
2,020
583
25,692
28,295
A person is selected at random from the sample. Find the probability of each event:
a. The person had a cold
b. The person had a cold or the flu
c. The person had neither illness, given that the person is a smoker
d. The person had a cold, given that the person is a smoker
e. The person is a smoker, given that the person had a cold
f. The person had the flu and is a smoker
g. The person had the flu or is a smoker
Which event(s) in Exercise 1 can be considered unusual? Explain your reasoning.
A person is selected at random from the sample in Exercise 1. Based on the answers from Part (a) and Part (d) above, determine whether the events “the person had a cold” and “the person is a smoker” are independent or dependent. Explain your reasoning.
A person is selected at random from the sample in Exercise 1. Are the events "the person had a cold" and "the person is a smoker" mutually exclusive? Explain your reasoning.
(Bonus Question - 10 points) You are given P(A)=0.85 and P(B)=0.45. Can these two events be mutually exclusive? If not explain why not.
Colds
Flu
Neither
Total
Smoker
526
153
4,980
5,659
Nonsmoker
1,494
430
20,712
22,636
Total
2,020
583
25,692
28,295
Explanation / Answer
a)
A person is selected at random from the sample. Find the probability of each event:
a. The person had a cold
Using the table,
P = 2020/28295 = 0.071390705 [ANSWER]
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b. The person had a cold or the flu
Using the table,
P = (2020+583)/28295 = 0.091995052 [ANSWER]
c. The person had neither illness, given that the person is a smoker
Using the table,
P = 4980/5689 = 0.875373528 [ANSWER]
d. The person had a cold, given that the person is a smoker
Using the table,
P = 526/5689 = 0.092459132 [ANSWER]
**************************************
e. The person is a smoker, given that the person had a cold
Using the table,
P = 526/2020 = 0.26039604 [ANSWER]
************************************
f. The person had the flu and is a smoker
Using the table,
P = 153/28295 = 0.005407316 [ANSWER]
************************************
g. The person had the flu or is a smoker
Using the table,
P = (526+153+4980+430)/28295 = 0.215197031 [ANSWER]
*******************************************
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