Question 1

Two events are said to be disjoint or mutually exclusive when they have no outcomes in common.

Accepted Answer

Two events are said to be disjoint or mutually exclusive when they have no outcomes in common. Therefore, the statement is true.

Question 2

Any collection of possible outcomes of a chance experiment is called a sample space.

Accepted Answer

A sample space is the set of all possible outcomes of a chance experiment, not just any collection of them.

Question 3

A chance experiment is any activity or situation in which there is uncertainty concerning which of two or more possible outcomes will result.

Accepted Answer

A chance experiment involves uncertainty about the outcome, which means there are multiple possible outcomes. Therefore, the statement is true.

Question 4

The probability of an event E can always be computed using the formula, ​

Accepted Answer

The formula given is not a valid formula for computing the probability of an event. The correct formula for computing the probability of an event is P(E) = (number of favorable outcomes)/(number of possible outcomes).

Question 5

With the advent of cable television, a tremendous number of channels and wide variety of programs are available for viewing. Consider an experiment where the weekly TV listings are located, a random page is chosen, and a random point on the page is picked. The outcome of the experiment is whatever program is described at that point on the page. Define events P₁, P₂, and P₃ as follows: P₁ = the program is an educational program P₂ = the program is on a regular network channel, not cable P₃ = the program is intended for children For each problem below, sketch a standard Venn diagram with 3 circles and shade the regions that correspond to the following events: a) An educational program for adults is selected. b) A children's program is selected. c) A network educational program for children is selected.

Accepted Answer

The answer of With the advent of cable television, a...

Question 6

Consider the chance experiment in which a high school principal selects a sports event at random to attend. The sex of the participants (Male or Female) is noted, as well as the type of event (Wrestling, Volleyball, Basketball, or Swimming). a) Display the possible outcomes of this selection using a tree diagram. b) Let M be the event that the participants are male and B be the event that a ball is involved (i.e. basketball or volleyball). i) What outcomes are in B^C? ii) What outcomes are in ? iii) What outcomes are in ?

Accepted Answer

The answer of Consider the chance experiment in which a...

Question 7

A statistics class conducts a chance experiment in which they observe students who buy a snack and the school vending machines. The type of food (Liquid, or Solid) is noted, as well as the number of calories of fat content (25, 50, or 75). a) Display the possible outcomes using a tree diagram. b) Let L be the event that the item is liquid and B be the event that the item has fewer than 75 calories of fat. i) What outcomes are in B^C? ii) What outcomes are in ? iii) What outcomes are in ?

Accepted Answer

The answer of A statistics class conducts a chance experiment...

Question 8

If two events, A and B, are disjoint, then  .

Accepted Answer

The answer of If two events, A and B, are...

Question 9

The classical view of probability is based on the Law of Large Numbers.

Accepted Answer

The classical view of probability is based on the assumption of equally likely outcomes, not the Law of Large Numbers, which pertains to the stability of averages from large samples.

Question 10

In order to ensure the safety of school classrooms the local Fire Marshall does an inspection at Thomas Jefferson High School every month, looking for faulty wiring, overloaded circuits, etc. At TJHS the new Academic Wing has 5 math rooms, 10 science rooms, and 10 English rooms. The science rooms are divided into 8 biology and 2 chemistry rooms. Each month, the Fire Marshall randomly picks one of the rooms in the new wing to inspect each month. Define the following events: S = the event the selected room is a science room B = the event the selected room is a biology room M = the event the selected room is a math room E = the event the selected room is an English room C = the event the selected room is a chemistry room Calculate the probabilities of the events described below: 
a) P(S) 
b) P(M or E ) 
c) P(E or B) d) P(S and not C)

Accepted Answer

The answer of In order to ensure the safety of...

Question 11

Two events are independent if they cannot occur simultaneously.

Accepted Answer

Two events are independent if the occurrence of one event does not affect the probability of the other event occurring. They can still occur simultaneously.

Question 12

As it gets close to time for school to start, automobiles begin to arrive on campus. Consider an experiment where a vehicle is selected at random. Define events as follows: V₁ = the vehicle belongs to a school staff member V₂ = the vehicle is less than 5 years old V₃ = the vehicle is American made For each problem below, sketch a standard Venn diagram with 3 circles and shade the regions that correspond to the following events: a) An American vehicle less than 5 years old is selected. b) A staff member's vehicle is selected. c) An American made staff member's vehicle at least 5 years old is selected.

Accepted Answer

The answer of As it gets close to time for...

Question 13

A small manufacturing firm has 250 employees. Fifty have been employed for less than 5 years and 125 have been with the company for over 10 years. Suppose that one employee is selected at random from a list of the employees. For the following events, compute the probabilities requested below. A = the event the selected employee has been with the firm less than 5 years B = the event the selected employee has been with the firm 5 ≤ x ≤ 10 years. C = the event the selected employee has been with the firm over 10 years. ​ 
a) P(A) 
b) P(C) 
c) P(A or B) d) P(A and C)

Accepted Answer

The answer of A small manufacturing firm has 250 employees....

Question 14

The General Addition Rule states that ​

Accepted Answer

The General Addition Rule, also known as the Addition Rule for Mutually Exclusive Events, states that if two events are mutually exclusive, the probability of either occurring is the sum of the probabilities of each individual event.

Question 15

Two events, E and F, are independent if  .

Accepted Answer

The answer of Two events, E and F, are independent...

Question 16

In a few sentences, distinguish between the classical and relative frequency approaches to probability.

Accepted Answer

The answer of In a few sentences, distinguish between the...

Question 17

An event consisting of exactly one outcome is called a simple event.

Accepted Answer

A simple event is an event where only one outcome can occur. Therefore, it consists of exactly one outcome.

Question 18

The event "A or B" consists of all of the outcomes in both of the events.

Accepted Answer

The event "A or B" consists of all the outcomes in either event, not both.

Question 19

In a few sentences, define the following terms: a) Sample space b) Disjoint events

Accepted Answer

The answer of In a few sentences, define the following...

Question 20

The General Multiplication Rule states that  .

Accepted Answer

The General Multiplication Rule states that the probability of the intersection of two events is equal to the product of their individual probabilities if the events are independent.

Quiz 6: Probability

Two events are said to be disjoint or mutually exclusive when they have no outcomes in common.

Any collection of possible outcomes of a chance experiment is called a sample space.

A chance experiment is any activity or situation in which there is uncertainty concerning which of two or more possible outcomes will result.

The probability of an event E can always be computed using the formula, ​

If two events, A and B, are disjoint, then .

The classical view of probability is based on the Law of Large Numbers.

Two events are independent if they cannot occur simultaneously.

The General Addition Rule states that ​

Two events, E and F, are independent if .

In a few sentences, distinguish between the classical and relative frequency approaches to probability.

An event consisting of exactly one outcome is called a simple event.

The event "A or B" consists of all of the outcomes in both of the events.

In a few sentences, define the following terms: a) Sample space b) Disjoint events

The General Multiplication Rule states that .

The probability of an event E can always be computed using the formula,

The General Addition Rule states that