In a large accounting firm, the proportion of accountants with MBA degrees and at least 5 years of professional experience is 0.75 times the proportion of accountants with no MBA degree and less than 5 years of professional experience. Furthermore, 35% of the accountants in this firm have MBA degrees, and 45% have less than 5 years of professional experience.
(a) What is the probability of a randomly selected accountant to have at least 5 years of professional experience?
(b) What proportion of accountants with MBA degrees have at least 5 years of professional experience?
(c) What is the probability of a randomly selected accountant to have at least 5 years of professional experience and no MBA degree?
(d) If one of the firm's accountants is selected at random, what is the probability that this accountant has an MBA degree or at least 5 years of professional experience but not both?
We are given P(MBA)=0.35, so P(no MBA)=1-0.35=0.65.
P(less than 5 years | MBA)=0.45 , so P(at least 5 years | ...
The solution gives detailed steps on calculating the conditional probability under different conditions using contingency tables.
Define (a) random experiment, (b) sample space, (c) simple event, and (d) compound event.
1. Define (a) random experiment, (b) sample space, (c) simple event, and (d) compound event.
2. What are the three approaches to determining probability? Explain the differences among them.
3. Sketch a Venn diagram to illustrate (a) complement of an event, (b) union of two events, (c) intersection of two events, (d) mutually exclusive events, and (e) dichotomous events.
4. Define odds. What does it mean to say that odds are usually quoted against an event?
5. (a) State the additive law. (b) Why do we subtract the intersection?
6. (a) Write the formula for conditional probability. (b) When are two events independent?
7. (a) What is a contingency table? (b) How do we convert a contingency table into a table of relative frequencies?
8. In a contingency table, explain the concepts of (a) marginal probability and (b) joint probability.
9. Why are tree diagrams useful? Why are they not always practical?
10. What is the main point of Bayes's Theorem?
11. Define (a) fundamental rule of counting, (b) factorial, (c) permutation, and (d) combination.