MS5030: Practice problems – Set I
1. A bank classifies borrowers as high-risk or low-risk. Only 15% of its loans are made to those in high-risk category. Of all its loans, 5% are in default, and 40% of those in default were made to high-risk borrowers. What is the probability that a high-risk borrower will default?
2. A fund manager is considering investing in the stock of a healthcare provider. The manager’s assessment of probabilities of the rates of return on this stock over the next year is summarized in the table below. |Rate of return |Less than -10% |-10% to 0% |0% to 10% |10% to 20% |More than 20% | |Probability |0.04 |0.14 |0.28 |0.33 |0.21 |
Let A be the event “Rate of return will be more than 10%,” and B be the event “Rate of return will be negative.” • Find the probability of events A and B.
• Describe the even that is complement of event A.
• Find the probability of the complement of A.
• Describe the even that is complement of event B.
• Find the probability of the complement of B.
• Describe and find the probability of event that is intersection of A and B. • Describe and find the probability of event that is union of A and B. • Are events A and B mutually exclusive? Collectively exhaustive?
3. A random sample of 52 personal property insurance policies showed the following number of claims over the last year: |# of claims |0 |1 |2 |3 |4 |5 |6 | |# of policies |21 |15 |5 |4 |2 |3 |2 |
• Find the mean number of claims per day.
• Find the sample variance and standard deviation.
4. A survey carried out for a supermarket classified customers according to whether their visits to the store are frequent or infrequent and whether...
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