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Unformatted text preview: NAME: Stat 205 Quiz 3
The following table crossclassiﬁes 6549 subjects living in Massachusetts according to health risk
(stressed or not stressed) and income (low, medium, or high):
Stress level
Stressed
Not Stressed
Total Income
Low Medium High
526
274
216
1954
1680
1899
2480
1954
2115 Total
1016
5533
6549 This is turned into a table of probabilities by dividing each cell by the total sample size 6549:
Stress level
Stressed
Not Stressed
Total Income
Low Medium High
0.08
0.04
0.03
0.30
0.26
0.29
0.38
0.30
0.32 Total
0.15
0.85
1.00 Let S be the event that a randomly selected individual is stressed and let L be the event that a
randomly selected individual has low income. Use the table to answer the following questions.
1. (2 points) What is the probability that someone in this study is stressed, P (S )?
Answer:
1016
= 0.15 (ﬁrst table) or 0.15 (second table).
6549
2. (2 points) What is the probability that someone with a low income in this study is stressed,
P (S L)?
Answer:
526
0.08
= 0.21 (ﬁrst table) or
= 0.21 (second table).
2480
0.38
3. (2 points) What is the probability that someone in this study is stressed or has low income,
P (S ∪ L)?
Answer:
526 + 274 + 216 + 1954
= 0.45 (ﬁrst table) or 0.08 + 0.04 + 0.04 + 0.30 (second table).
6549
You can also use the formula
P (S or L) =
=
=
= P (stressed or low income)
P (stressed) + P (low income) − P (stressed and low income)
0.15 + 0.38 − 0.08
0.45. 4. (2 points) Use (1) and (3) to determine whether being stressed and having low income are
independent.
Answer: P (stressedlow income) = P (stressed) so they are dependent, i.e. not independent. 5. (2 Extra credit points) Is having low income independent of having high income? Why or
why not?
Answer: They are disjoint events, so they are dependent. If you have low income, you cannot
have high income (P (low incomehigh income) = 0), one event tells you everything about
the other. Formally,
P (low incomehigh income) = P (low income) implies dependence. ...
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 Fall '09
 Hendrix
 Probability, Massachusetts

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