Topic 1: Combinatorics

1. Out of six computer chips, two are defective. How many ways of choosing exist, if two chips are randomly chosen for testing (without replacement). List all the outcomes in the sample space.

Topic 2: Total probability rule Bayes law

2. Financial analysts predict that next month with a probability of 0.5 there will be an increase in the stock price of Bank A, with a probability of 0.3 the stock price will remain unchanged, and the probability of a fall in the stock price of this bank is 0.2. If the stock price rises, one should expect an increase in capital in deposit accounts by 20%; if the exchange rate does not change, the amount of capital in deposit accounts is expected to be the same as in the previous month; and in the event of a depreciation, a decrease in the volume of capital on deposit accounts by 15% is expected. Determine the expected change in the amount of capital in the deposit accounts of this bank in the next month.

Topic 3: Discrete distributions

3. The quality control manager of Marilyn s Cookies is inspecting a batch of chocolate-chip cookies that has just been baked. If the production process is in control, the mean number of chip parts per cookie is 6.0. What is the probability that in any particular cookie being inspected?

a. less than five chip parts will be found?

b. exactly five chip parts will be found?

c. five or more chip parts will be found?

d. either four or five chip parts will be found?