Statistics

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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

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