Section 3.1 Part 1: Terminology (Probability)

A car dealership finds that a certain model of new car has something wrong with its transmission 15% of the time. How likely is it that a particular model of that car has something wrong with its transmission?

Somewhat unlikely, the probability is closer to 0 than it is to 1. Here, we would be most correct to say that the probability is somewhat unlikely . - It is not closer to 1 than it is to 0, so it is not appropriate to call it "likely" or "somewhat likely." - It is not very close to 0, so it is not quite appropriate to call it "unlikely". - It is false to call it "equally likely" since the probability isn't 0.5. We settle on "somewhat unlikely," since it is closer to 0 than to 1 but isn't that close to zero.

People with some college education stay married to their spouses for at least twenty years at a rate of 67%. How likely is it that a randomly selected, college educated couple will be married for at least twenty years? Select the correct answer below: Very likely, the probability is close to 1. Somewhat likely, the probability is closer to 1 than to 0. Unlikely, the probability is close to 0. Somewhat unlikely, the probability is closer to 0 than it is to 1. Equally likely, the probability is 0.5.

Somewhat likely, the probability is closer to 1 than to 0. Here, we would be most correct to say that the probability is somewhat likely . - It is not closer to 0 than it is to 1, so it is not appropriate to call it "unlikely" or "somewhat unlikely." - It is not very close to 1, so it is not quite appropriate to call it "likely". - It is false to call it "equally likely" since the probability isn't 0.5. We settle on "somewhat likely," since it is closer to 1 than to 0 but isn't that close to 1.

Three fair coins are flipped at the same time. Each coin has the two possible outcomes: heads or tails. There are 8 possible outcomes for the three coins being flipped: {HHH,TTT,HHT,HTT,THH,TTH,HTH,THT}. Let A be the event that the second coin flipped shows a head. Identify the numbers of each of the following: There are ______ outcomes in the sample space. There are ______ outcomes in event A. P(A)=_________​, is the probability that the second coin flipped shows heads.

The sample space is the set of all possible outcomes of an experiment. Here, there are 8 possible outcomes. The event is a grouping of the outcomes in the sample space. Here, event A is defined as the event of flipping a heads on the second coin. There are 4 outcomes in event A: A={HHH,HHT,THH,THT}. The probability that the second coin flipped shows heads is the comparison of being assigned to event A versus all the possible outcomes: P(A)=4/8=1/2.

There are 52 cards in a standard deck of cards, with four of each type of card: Ace ,2,3,4,5,6,7,8,9,10,Jack ,Queen ,King . Let event A be choosing a 7 out of a deck of cards. Identify the numbers of each of the following. Enter the probability as a fraction: There are ________ cards in the sample space. There are ________ cards in event A. P(A)=________​, is the probability that you choose a 7 out of the deck of cards.

There are 52 cards in the sample space. There are 4 cards in event A. P(A)= 452​, is the probability that you choose a 7 out of the deck of cards. The sample space is the set of all possible outcomes of an experiment. Here, there are 52 possible cards. The event is a grouping of the outcomes in the sample space. A is defined as the event of drawing a 7. Here, there are four 7 cards. The probability of a drawing a 7 is the comparison of drawing a 7 to all the possible outcomes, P(A)=4/52=1/13.

A CEO decides to award her employees that have met their objectives this year. Those employees that have met their objectives have the chance to win vacation days. They can win either Mondays (abbreviated M) or Tuesdays (abbreviated T). They can also win up to two days. The Venn Diagrams below show the different combinations that an employee can win. - Let A be the event of winning two of the same day. - Let B be the event of winning a Monday Move the dots on the Venn diagram to place the dots in the correct event, A, B,or A AND B. Note that you might not use all of the dots.

- Event A is the event of winning two of the same day, so A should contain elements with repeated letters. - Event B is the event of winning at least one Monday, so B should contain outcomes with the letter M . - Event A AND B should therefore contain the outcome with two Mondays. Notice that the outcomes T does not fall into either of these events. It should therefore be outside of the Venn diagram.

Each side of a fair, six-sided die has a certain number of dots on it, 1,2,3,4,5, or 6. The die is rolled by a board game player as part of their turn. Identify the correct experiment, trial, and outcome below: - The experiment is identifying the number that is rolled on the die. - The experiment is rolling the die. - A trial is one rolling of the die. - The trial is identifying the number on the die. - The outcome is rolling the die. - The outcome is the number that is rolled on the die.

Correct answer: - The experiment is rolling the die. - A trial is one rolling of the die. - The outcome is the number that is rolled on the die. - An experiment is a planned operation carried out under controlled conditions. Here, rolling the die is the experiment. A trial is one instance of a an experiment taking place. A trial here is one rolling of the die. An outcome is any of the possible results of the experiment. Here, the outcome is any of the numbers on the die.

A computer randomly generates numbers 1 through 100 for a lottery game. Every lottery ticket has 7 numbers on it. Identify the correct experiment, trial, and outcome below: Select all that apply: - The experiment is the computer randomly generating a number. - The experiment is the computer randomly generating a number less than 10. - A trial is one number generated. - The trial is identifying the number generated. - An outcome is the number 2 being generated. - The outcome is the number being randomly generated.

Correct answer: The experiment is the computer randomly generating a number. A trial is one number generated. An outcome is the number 2 being generated. An experiment is a planned operation carried out under controlled conditions. Here, generating a random number is the experiment. A trial is one instance of a an experiment taking place. A trial here is one number being generated. An outcome is any of the possible results of the experiment. Here, the outcome is any of the numbers between 1 and 100.

There are 150 new employees at a tech company in Southern California. 30 new employees are randomly assigned to each orientation group: A,B,C,D, and E. Identify the numbers of each of the following: Provide your answer below: There are _______ new employees in the sample space. There are _______ new employees in each event. P(C)=________, is the probability that you choose new employee that has been assigned to orientation group C.

Correct answers: The sample space is the set of all possible outcomes of an experiment. Here, there are 150 possible employees. The event is a grouping of the outcomes in the sample space. Here, there are 30 employees in each event: A,B,C,D,E. The probability of a new employee being assigned to group C is the comparison of being assigned to group C versus all the possible groups: P(C)=30/150=1/5.

The average emergency room cares for 300 patients each day. There are 20 nurses on duty at the emergency room each day, and they share the patient load equally. Suppose one patient is chosen at random. Identify the numbers of each of the following and enter the probability as a simplified fraction: There are _______ patients in the sample space. There are ______ patients for each nurse daily. P(N)=_______​, is the probability that a patient will be assigned to a specific nurse.

Correct answers: The sample space is the set of all possible outcomes of an experiment. Here, there are 300 possible patients. The event is a grouping of the outcomes in the sample space. Here, there are 15 possible patients that a nurse may have. The probability of a patient being assigned to a specific nurse, N, is the comparison of being assigned to that nurse's patients versus all possible patients: P(N)=15/300=1/20.

A mathematics professor is organizing her classroom into groups for the final project. Each student will either be working on a graphing (G) project or writing a paper (P). Also, each student will be working on an economics (E), finance (F), sociology (S), or criminal justice (C) problem. The dots in the Venn diagram below show the different scenarios. Let A be the event of a student working on a graphing project. Let B be the event of a student writing a paper. Move the dots on the Venn diagram to place the dots in the correct event, A, B,or A AND B. Note that you might not use all of the dots.

Event A is the event of a student working on a graphing project, so A should contain all outcomes with a G. Event B is the event of a student writing a paper, so B should contain all outcomes with a P. Event A AND B should therefore contain all outcomes with both a P and a G; however, none exist. Notice also that nothing should be outside of the Venn Diagram because every project is either a graphing project or a paper.