Practice Prob 1 - Dam

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