An electronics company is about to launch a new product. If the serial number for each piece produced has the following format: LLNNN where L stands for any letter in the English alphabet and N is a number from 0 to 9, please answer the following:

a)What is the name of the counting rule used to find all the possible outcomes?

b)How many different items can be uniquely numbered?

2)

(5 pts)

A company needs to select an expert group of consultants to provide advice for a given project. How many possible selections consisting of 2 project managers, 2

legal advisors, 4 computer scientists and 3 systemsengineers can be selected if the company can pick from 4 project managers, 7 legal advisors, 5 computer scientists and 6 systems engineers? Think carefully about the counting rules involved before attempting to do any calculations.

3)

(5 pts)

Consider that you are a line manager in your current Corporation. There is a 0.50 probability that you will be promoted this year. There is a 0.65 probability that you will get a promotion or a raise. The probability of getting a promotion and a raise is 0.35. (Use letter P to denote promotion and letter R to denote raise.)

a. If you get a promotion, what is the probabilitythat you will also get a raise?

b. What is the probability that you will get a raise?

c. Are getting a raise and being promoted independent events? Explain using

probabilities.

d. Are these two events mutually exclusive? Explain using probabilities.

Please show all the steps in your calculations

Part 2

Two of the cylinders in an eight-cylinder car are defective and need to be replaced. If two

cylinders are selected at random, what is the probability that

a. both defective cylinders are selected?

b. no defective cylinder is selected?

c. at least one defective cylinder is selected?

You are requested to solve the problem using two different approaches:

1.(9 pts) Solve the problem using your knowledge from the theory of probability (chapter 4 in your e-text). If you wish to use letters in order to label the events: please let "D

1

" denote the event of the first cylinder selected, to be defective and let "D

2

" denote the event of the second cylinder selected, to be defective. If you find it helpful

you can construct a tree diagram for this problem.

2.(9 pts) Solve the problem using your knowledge on probability distributions (chp 5 &

6). It is important to justify your choice of probability distributionto use. You will need to decide whether your random variable is continuous or discrete and also need to identify whether the sampling carried out is with or without replacement. These steps will help you to identify the appropriate probability distribution to use.

3.(2 pts) Finally compare the two solutions. Elaborate on thecomputational complexity

of each one of them and the execution time when solving the problem by hand (allowing the use of a basic scientific calculator but not statistical software).

#### Top Answer

Dear pkawesha, PFA for... View the full answer