Question

1. A State issues car license plates with three letters followed by three numbers (for example, FGH831 or BBB222). How many different license plates are possible? (Note that letters or numbers may repeat in the license plate. Hint: Use the Fundamental Counting Rule for this question.)

There are five students who are interested in presenting their final project to the class, but there is only time for three presentations. The five students are Amy, Bob, Chun, Dan and Ed.

2. List all the possible combinations of three students the professor could pick. The order of the presentations does not matter. To save space, you can just use the first initial of each name if you like.

3. How many different combinations are there?

4. Now, use the Counting Rule for Combinations formula to calculate the number of combinations and compare your results.

5. Which approach was easier?

6. If the professor picks three students at random by drawing three names from a hat, what is the probability that the three students chosen are Amy, Chun and Dan?

Now, assume that the first student chosen will present on Monday, the second will present on Wednesday and the third will present on Friday. In other words, now the order the students are chosen matters. Use this situation to answer questions 7, 8 and 9.

7. If the professor chooses Amy, Chun and Dan to present, list all the possible permutations of how their presentations could be distributed over the three days.

8. Use the Counting Rule for Permutations formula to calculate the total number of permutations when the professor is picking three students from the original group of five and the order matters.

9. If the professor picks three students at random from the original group of five, what is the probability that the results will be that Bob will present on Monday, Ed will present on Wednesday and Chun will present on Friday?

A San Francisco business finds that the probability that one of its employees is a good employee is .50, and that the probability the employee is OK is .30 and the probability the employee is bad is .20. These are the prior probabilities, and these three events are mutually exclusive and exhaustive. In other words, any particular employee will be in one of these categories, but only one category. The business looks at their employees’ backgrounds and finds that the probability that a good employee attended City College is .72. In other words, the probability that the employee attended City College, given that the employee is good, is .72. The probability that an OK employee attended City College is .40, and the probability that a bad employee attended City College is .00. Event Q_G means the employee is good, event Q_OK means the employee is OK and event Q_B means the employee is bad. Event C means the employee attended City College.

Hint: Use the multiplication law to calculate the following three problems.

10. Compute P(C ∩ Q_G).

11. Compute P(C ∩ Q_OK).

12. Compute P(C ∩ Q_B).

13. A new employee who attended City College starts work at the business. Use Bayes’ Theorem to determine the probability that this new employee will be good, OK or bad. In other words, find P(Q_G| C), P(Q_OK| C) and P(Q_B| C).

14. If you were the HR director for this business, what action would you take as a result of this statistical analysis?

Answer 1

As per Chegg guidlines we should answer only first question. Please post the other questions differently