Econ 101 Discussion Assignment #2
1. The probability that a UCR graduate finds a job within six months (Event A) is 0.72 . The probability that a UCR graduate lives in Los Angeles County (Event B) is 0.37. The probability that a UCR graduate finds a job within six month and lives in Los Angeles County is 0.21.
a. What is the probability that a UCR graduate did not find a job in six months and lives in Los Angeles county? Label the part of the sample space that corresponds to this probability. Calculate the probability.
b. What is the probability that a student finds a job within six months or lives in Los Angeles county? Label the part of the sample space that corresponds to this probability. Calculate the probability.
c. Given that a UCR graduate lives in Los Angeles county, what is the probability they found a job within six months?
2. A survey of business professionals collected information on the position and tasks of the respondents. The following table summarizes the responses (fill in the blanks):
|
|
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Position
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Analyze data?
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Entry Level
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Manager
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Total
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Yes
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205
|
22
|
|
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No
|
44
|
35
|
|
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Total
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|
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|
a. What is the probability that a randomly selected professional analyzes data?
b. What is the probability that a randomly selected professional is entry level and analyzes data?
c. Given that a professional is entry level, what is the probability that the professional analyzes data?
d. Is analyzing data and being entry level independent? Explain.
3. The outcome of the presidential election often hinges on keyswing states. The
probability Kamala Harris wins the state of Pennsylvania is .52. If Harris wins Pennsylvania, the probability that Harris wins the national election is 0.65. If Harris loses in Pennsylvania, the probability that Harris wins the national election is .45.
a. Label the following tree diagram to visualize the sample space. Label the probabilities and calculate any missing values.
b. What is the probability that Harris wins Pennsylvania and wins the national election? Highlight the path on the tree.
c. What is the probability that Harris loses Pennsylvania and wins the national election? Highlight the path on the tree.
d. What is the probability that Harris wins the national election?
e. Given that Harris wins the national election, what is the probability that she won Pennsylvania?