Probability And Counting Rules Essay

Probability and Counting Rules

The relevant R codes and outputs must be attached for full credit.

1. Explain whether or not the following numbers could be examples of a probability.

(8 points total 2 points each)

a) P(A) = 0.5

b) P(B) = 0

c) P(C) = 1.6

d) P(D) = -3

2. A quality control engineer randomly selects two light bulbs from a shipment to determine if they meet all the specifications defined by a company. Let M = a light bulb meets all the specifications defined by a company, and N = a light bulb does NOT meet all the specifications defined by a company. Write the sample space of this experiment in set notation. (1 point)

3. Consider x be an event defined by the waiting time (in hours) between successive speeders spotted by a radar unit. Write the sample space of this event using mathematical notation. (1 point)

4. Consider the sample space S = {copper, sodium, nitrogen, potassium, uranium, oxygen, zinc} and the events

A = {copper}

B = {sodium, nitrogen, potassium}

C = {oxygen}

List the elements of the sets corresponding to the following events using set notation:

Source: Walpole, R.E., Myers, R.H., Myers, S.L., & Ye, K. (2012). Probability & Statistics for Engineers & Scientists. Boston, MA: Pearson.

a. BC (1 point)

b. A B C (1 point)

c. (A B)C (AC C) (1 point)

d. B C (1 point)

5. A drug for the relief of asthma can be purchased from 5 different manufacturers in liquid, tablet, or capsule form, all of which come in regular and extra strength. How many different ways can a doctor prescribe the drug for a patient suffering from asthma? (1 point)

6. A developer of a new subdivision offers a prospective home buyer a choice of 4 designs, 3 different heating systems, a garage or carport, and a patio or screened porch. How many different plans are available to this buyer? (1 point)

7. How many distinct ways are there to arrange the letters of the word “Miami”? (Note: Assume capital M and lowercase m are the same letter) (1 point)

Note: Students can use RStudio or a formula.

8. A statistics class for engineers consists of 53 students. The students in the class are classified based on their college major and sex as shown in the following contingency table:

Probability And Counting Rules Essay

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