# Chapter 4 Notes

CH4

Counting Rule: mn

Sampling with replacement: N^n

Sampling without replacement: NCn

Combination formula: NCn = N!/n!(N-n)!

General Law of addition: P (X∪Y) = P(X) + P(Y) – P (X∩Y)

Special Law of addition: P (X∪Y) =P(X) +P(Y)

General Law of multiplication: P (X∩Y) = P(X) ▪P (YIX) = P(Y) ▪P (XIY)

Special Law of multiplication: P (X∩Y) = P(X) ▪P(Y)

Law of conditional probability: P(XIY)= (P (X∩Y))/(P(Y))=(P(X)▪P(YIX))/(P(Y))

Bayes’ rule:

Experiment: Process that produces outcomes

Event: An outcome of an experiment

Priori: Can be determined prior to an experiment

Classical method: Probabilities assigned based on laws and rules; P(E)= ne/N

Relative Frequency of Occurrence: # of times event occurred/ Total # of opportunities for the event to occur

Subjective method: Based on feelings, insight, intuition

Elementary events: Events that cannot be broken down into other events.

Sample space: Complete roster/listing of all elementary events for an experiment.

Intersection: Contains elements common to both sets

Mutually exclusive events: Occurrence of one precludes the occurrence of the other event(s)

Independent events: If the occurrence or non-occurrence of an event has no effect on the other

Collectively exhaustive events: Contain all possibly elementary events for an experiment

Complement of event A: All the elementary events of an experiment not in A comprise its complement

Probability matrix: Displays the margina l probabilities and the intersection probabilities of a given problem

1) Probability is used to develop knowledge of the fundamental mathematical tools for quantitatively assessing risk. T

2) Assigning probabilities by dividing the number of ways that an event can occur by the total number of possible outcomes in an experiment is called the classical method. T

3) Which of the following statements is not true regarding probabilities?: probabilities are subjective measures with limited value in business.

4) Which of the following is not a legitimate probability value? 5/4

5) Which of the following is a legitimate probability value? 0.28

6) Assigning probability 1/52 on drawing the ace of spade in a deck of cards is an example of assigning probabilities using: classical probability

7) In a set of 25 aluminum castings, four castings are defective (D), and the remaining twenty-one are good (G). A quality control inspector randomly selects three of the twenty-five castings without replacement, and classifies each as defective (D) or good (G). The sample space for this experiment contains elementary events. NCn = N!/n!(N-n)! => NCn = 25!/3!(25-3)!=2300

8) In a set of 12 aluminum castings, two castings are defective (D), and the remaining ten are good (G). A quality control inspector randomly selects three of the twelve castings with replacement, and classifies each as defective (D) or good (G). The sample space for this experiment contains __ elementary events. 12^3=1728

9) Consider the following sample space, S, and several events defined on it. S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}. F∩H is ___? {Meagan}(and sign means only one that repeats)

10) Consider the following sample space, S, and several events defined on it. S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}. F U H (U for Union) is ___.{Betty,Abel,Patty,Meagan} (U list all)

11) Consider the following sample space, S, and several events defined on it. S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}. The complement of F is ___. {Albert,Abel,Jack}

12) Which is not true? Airlines and healthcare are collectively exhaustive

13) The number of different committees of 2 students that can be chosen from a group of 5 students is 10

14) Let F be the event that a student is enrolled in a finance course, and let S be the event that a student is enrolled in a statistics course. It is known that 40% of all students are enrolled in a finance course and 35% of all students are enrolled in statistics. Included in these numbers are 15% who are enrolled in both statistics and finance. Find the probability that a student is in finance and is also in statistics.0.15

15) Let F be the event that a student is enrolled in a finance course, and let S be the event that a student is enrolled in a statistics course. It is known that 40% of all students are enrolled in a finance course and 35% of all students are enrolled in statistics. Included in these numbers are 15% who are enrolled in both statistics and finance. A student is randomly selected, what is the probability that the student is enrolled in either finance or statistics or both? (0.35+0.40)-0.15=0.60

16) Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the Plano Power Plant. Ten percent of all plant employees work in the finishing department; 20% of all plant employees are absent excessively; and 7% of all plant employees work in the finishing department and are absent excessively. A plant employee is selected randomly; F is the event “works in the finishing department;” and A is the event “is absent excessively.” P(A U F) = _. (0.20+0.10)-0.07=0.23

17) A market research firm is investigating the appeal of three package designs. The table below gives information obtained through a sample of 200 consumers. The three package designs are labeled A, B, and C. The consumers are classified according to age and package design preference.

Are “B” and “25 or older” independent and why or why not? No, because P (25 or older | B) ≠ P (25 or older)

18) Suppose 5% of the population have a certain disease. A laboratory blood test gives a positive reading for 95% of people who have the disease and 10% positive reading of people who do not have the disease. . What is the probability that a randomly selected person has the disease given that this person is testing positive? P(AlE)= P(A)xP(ElA) /( P(A) x P(ElA) + P(B) x P(ElB)) (.05x.95)/((.05x.95)+(.95x.10))= 0.333 BAYES RULE.