Question 1 - A computer software company has developed a new accounting program. The beta version of the program is being tested by 90 CPAs.
a. Define the experiment.
b. Define one possible outcome.
c. Define one possible event.
d. Suppose 81 out of 90 CPAs preferred this new program over the competing current accounting program they use. Is 81 the probability that the new program, if brought into the market, will be successful? If not, estimate the probability of success.
e. Suppose the probability that the new program fails, if brought into the market, is - 0.81. Can this be right? If not, compute the probability of failure.
Question 2 - The following table depicts salaries of presidents of 25 Fortune 500 companies and shareholders' profit or loss:
|
|
Salary more than $1 million
|
Salary less than $1 million
|
Total
|
|
Shareholders made Money
|
4
|
11
|
15
|
|
Shareholders lost Money
|
6
|
4
|
10
|
|
Total
|
10
|
15
|
25
|
If we select a company randomly, what is the probability that:
a. A president made more than $1 million?
b. A president made more than $1 million or shareholders lost money?
c. A president made more than $1 million given shareholders lost money?
d. We select two Presidents and find they both made more than $1 million?
Question 3 - Drivers applying to a fictional insurance company fall within three classifications of risks, good, medium, or poor, with the proportions of 40%, 40% and 20%, respectively. The probability that a good, medium, and poor risk driver will end up with exactly one accident is 0.02, 0.03, and 0.10, respectively. The company sells an insurance policy to Bob, who has a record of one accident. What is the probability that Bob is:
a. A "good risk" driver?
b. A "medium risk" driver?
c. A "poor risk" driver?
Question 4 - Summation Expressions - Calculate the following summation expressions:
1) i=1∑11i
2) i=1∑101i
3) i=1∑1,001i
4) i=1∑10,001i
5) i=1∑100,001i
6) i=1∑1,000,001i
7) Etc.
Can you find a pattern in the above sums of the numbers? If so, explain the pattern. Can you present the pattern in a mathematical formula? Can you generalize the pattern to the sums of numbers if the upper summation indices were 10,100, 1,000, 10,000, 100,000, 1,000,000, etc.?