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Unformatted text preview: NAME: Stat 205 Quiz 3
The following table cross-classiﬁes 6549 subjects living in Massachusetts according to health risk
(stressed or not stressed) and income (low, medium, or high):
Low Medium High
6549 This is turned into a table of probabilities by dividing each cell by the total sample size 6549:
Low Medium High
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 )?
= 0.15 (ﬁrst table) or 0.15 (second table).
2. (2 points) What is the probability that someone with a low income in this study is stressed,
P (S |L)?
= 0.21 (ﬁrst table) or
= 0.21 (second table).
3. (2 points) What is the probability that someone in this study is stressed or has low income,
P (S ∪ L)?
526 + 274 + 216 + 1954
= 0.45 (ﬁrst table) or 0.08 + 0.04 + 0.04 + 0.30 (second table).
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
Answer: P (stressed|low 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
Answer: They are disjoint events, so they are dependent. If you have low income, you cannot
have high income (P (low income|high income) = 0), one event tells you everything about
the other. Formally,
P (low income|high income) = P (low income) implies dependence. ...
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- Fall '09
- Probability, Massachusetts