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Probability Math115a and Sets Worksheet #3
Name:_______________________ #
Define all random variables used. Use correct mathematical notation. This worksheet is different since you have to calculate the probabilities from data given. Fill in the Venn Diagram with the given values, then answer the questions below. 1. A certain bank has collected the following records on its recent borrowers: 10 borrowers had at least 10 years experience, had an advanced degree and borrowed at least $3 million. 11 had an advanced degree and borrowed at least $3 million. 30 had an advanced degree. 17 had at least 10 years experience and had an advanced degree. 3 had at least 10 years experience, borrowed at least $3 million and did not have any advanced degrees. 2 had less than 10 years experience, had no advanced degrees and borrowed at least $3 million. 8 had less than 10 years experience, had no advanced degrees and borrowed less than $3 million. 16 had at least 10 years experience and borrowed less than $3 million.
a) How many borrowers are represented all together? If we randomly select a borrower from the banks records, find the probability that: b) the borrower has more than 10 years experience.
c) the borrower was loaned at least $3 million.
d) the borrower had no advanced degrees.
e) the borrower was loaned less than $3 million.
Worksheet 3 page 2 2. The following table shows the insurance status of female employees at various size companies. A sample of 10,000 employees was taken for each size category. You may assume that an employee can be counted under only one insurance status. Size of company 100-499 500-999 1000 or more Total Covered by Employer 6,220 6,720 7,048 Covered by Spouses Employer 1,500 1,490 1,175 Covered by private insurance 980 885 965 Uninsured Total
1,300 905 812
Determine the probability distribution if the outcome of interest is the insurance status a) Regardless company of size, what is the probability that an employee will be insured either by her employer or by her spouses employer?
b) For company sizes of 100-499, what is the probability that an employee will be insured either by her employer or by her spouses employer?
c) Regardless of company size, what is the probability that an employee is insured by her employer?
d) For company sizes of 500-999, what is the probability that an employee is uninsured?
e) Regardless of company size, what is the probability that an employee is insured by her private insurance or by her spouses employer?
f) For company sizes of 500-999, what is the probability that an employee has private insurance or is uninsured?
g) For company size of at least 1000, what is the probability that an employee is not covered by her spouses employer?
Worksheet 3 page 3 3. A statistical analysis of the wait (in minutes) at the checkout line of a certain supermarket yields the following probability distribution: Wait At most 3 More than 3 and at most 5 More than 5 and at most 10 More than 10 and at most 15 Probability 0.1 0.2 0.25 0.25
a) What is the probability of waiti...