Chapter 5 Homework

Given an experiment of a rolling a die and the event getting an even, which of the following would for a set of events that are collectively exhaustive?

Getting an odd Getting a number less than 6

Which of the following statements describes a probability? Select all that apply.

It is a number between 0 and 1, inclusive. It describes the relative likelihood that an event will occur.

Two Events are Independent If:

the occurrence of one has no effect on the probability of occurrence of the other

Which of the following is a characteristic of the classical approach to probability?

Probabilities assume outcomes of an experiment are equally likely.

What does it mean when an experiment has a set of events that are collectively exhaustive?

That at least one of the events MUST occur.

As the number of trials increases, what does the law of large numbers say about the probabilities.

The EMPIRICAL probability will approach the event's true probability. i.e. the outcomes of flipping a coin 1000 times.

Which one of the following conditions must be met to use the special rule of addition? I.e. P(A or B)= P(A)+P(B)

The events A and B must be mutually exclusive.

What does a joint probability measure?

The likelihood that two or more events will happen concurrently.

Two events are mutually exclusive if:

The occurrence of one event means the other can't occur at the same time. - one excludes the other

The value given for an empirical probability is based on:

The past history of outcomes from the experiment i.e. the frequency distribution.

Suppose a high school student needs a 30 on his ACT to get a particular scholarship. If the student makes a 30 on the ACT, but he may or may not get the scholarship. Which one of the following represents a CONDITIONAL PROBABILITY?

The probability he gets the scholarship given he makes a 30 on the ACT.

Which of the following is a subjective probability?

You apply for a particular job after graduation and you estimate your chance of getting the job at 83% You can't apply for the job many times to see how many times you get it.

Mary has tickets to a concert. She wants to give four of them to her friends. If she has eight friends and only gives one ticket to each person, how many different ways can she distribute them?

70 (nCr) (8C4)= 8!/4!(8-4)!

Which of the following best describes the meaning of "outcome" in the context of a probability experiment?

A particular outcome

If there are "m" ways of doing one thing, and "n" ways of doing another thing, the multiplication formula states that there are (m) × (n) ways of doing both.

(m) x (n) This is called the multiplication rule

Which of the following are true regarding the special rule of addition and the general rule of addition? Select all that apply.

- If the events are mutually exclusive, you can use the special rule of addition. -If the events are not mutually exclusive, you can use the general rule of addition.

A permutation is any agreement of (r) selected from (n) possible objects. Which of the following is true

-(r) can be greater than (n)

When you roll a die, the probability that the face with three dots will lie uppermost is 1/6. Use the compliment rule to find the probability that the upper face will NOT be a three.

5/6 P(~3)=1-P(3)=1-1/6

Choose the statement that best defines the term "experiment" in the context of probability:

A process that leads to only one of several outcomes.

The City Cafe is know for their vegetable plate lunch special which comes with four vegetable, corn bread, and sweet tea. If the four vegetables can be selected from a group of ten vegetables, what formula should be used to determine how many different vegetable plates there are?

Combination formula (nCr) This would require the combination formula because order does not matter.

A table used to classify observations according to two or more identifiable characteristics, and often used to to determine probabilities is called a _________ table.

Contingency

If the fraction of times an event happened in the past is used as the basis for assigning a probability to the event, this is _________ probability.

Empirical

A dice cube is tossed and the number of spots on the uppermost face is noted. Match the term

Experiment: The process of tossing the die Outcome: The die is a two Event: The die is greater than two