Week 7 Reading

We generally test for the independence of two events by comparing the conditional probability of one event, for instance P(A∣B), to the probability, P(A). If these two probabilities are the '_____' , we say that the two events, A and B, are independent; if the probabilities differ, the two events are '_____'.

- Blank 1: Same - Blank 2: Dependent

A random variable summarizes the results of an experiment in terms of numerical values and can be classified as '_____' or '_____' depending on the range of values that it assumes.

- Blank 1: discrete - Blank 2: continuous

Match each item on the left with the correct definition on the right: - Union of two events: - Intersection of two events: - Complement of event A:

- Union of two events: Denoted A ∪ B, is the event consisting of all outcomes in A or B. - Intersection of two events: Denoted A ∩ B, is the event consisting of all outcomes in A and B - Complement of event A: Denoted Ac, is the event consisting of all outcomes in the sample space S that are not in A

Match each probability concept with its definition: - probability: - experiment: - sample space:

- probability: a numerical value that measures the likelihood that an event occurs. - experiment: a process that leads to one of several possible outcomes. - sample space: contains all possible outcomes of the experiment.

Johnny feels that he has a 85% chance of getting an A in Marketing and a 45% chance of getting an A in Managerial Economics. He also believes he has a 35% chance of getting an A in both classes. What is the probability that he does not get an A in either of these courses?

.05

An economist predicts a 70% chance that country A will perform poorly and a 35% chance that country B will perform poorly. There is also a 20% chance that both countries will perform poorly. What is the probability that country A performs poorly given that country B performs poorly?

.20/.35 =.57

Johnny feels that he has a 85% chance of getting an A in Marketing and a 45% chance of getting an A in Managerial Economics. He also believes he has a 35% chance of getting an A in both classes. What is the probability that he gets an A in at least one of these courses?

.95 Reason: 0.85+0.45−0.35=0.95

Which of the following are the two defining properties of probability?

1. The probability of any event A is a value between 0 and 1; that is, 0 ≤ P(A) ≤ 1. 2. The sum of the probabilities of any list of mutually exclusive and exhaustive events equals 1.

In many instances, we calculate probabilities by referencing data based on the observed outcomes of an experiment. Which probability category is defined as the observed relative frequency with which an event occurs?

Empirical probability

True or false: The joint probability of events A and B is derived as P(A ∩ B) = P(A ∣ B)P(A).

False Reason: The joint probability of events A and B is derived as P(A ∩ B) = P(A ∣ B)P(B).

Two events are '_____' if the occurrence of one event does not affect the probability of the occurrence of the other event.

Independent

True or false: The probability that A occurs given that B has occurred is derived as P(A∣B)=P(A∩B)/P(B)

True

Which of the following defines a probability that is based on an individual's personal judgment or experience?

subjective probability

What do we refer to events which include all outcomes in the sample space?

Exhaustive

True or false: A discrete random variable is characterized by uncountable values, whereas a continuous random variable assumes a countable number of distinct values.

False

True or false: The sum of the probabilities of any list of mutually exclusive and exhaustive events do not always equal 1.

False

A manager believes that 20% of consumers will respond positively to the firm's social media campaign. Also, 24% of those who respond positively will become loyal customers. Find the probability that the next recipient of their social media campaign will react positively and will become a loyal customer?

P(R ∩ L) =P(L∣R)P(R) = 0.24 × 0.20 =.048

Because many choices we make involve some degree of uncertainty, we are better prepared for the eventual outcome if we can use '_____' to describe which events are likely and which are unlikely.

Probabilities or probability