STAT201: R4+HW4

For a class exercise, students conduct a probability experiment in which they toss a coin 5 times in a row. The probability of getting all tails is (check all that are correct):

(.5)^5

Which of the following cannot be a probability?

- -.34 -7/6 -6.58

Which value below could not be a probability?

-.12

Match the following examples with a type of probability.

-A die is rolled ten times and the number of threes recorded --> Empirical -The likelihood of a coin coming up heads--> Theoretical -The Yankees chances of winning the series--> Subjective

Match the following examples with a type of event.

-Cigarette smoking and developing lung cancer--> Dependent -Rolling "snake eyes" after rolling a string of sevens--> Independent

The types of probability include ________.

-Subjective probability -Theoretical probability -Empirical probability

Probability experiments all share what characteristic?

-They can have more than one possible outcome -Each possible outcome can be specified in advance -The outcome is due to chance

A marketing researcher for a small candy store is considering shopping behaviors. Which of the following are mutually exclusive events?

-deciding to shop or not shop at the store -buying candy or not buying candy

In the previous question, what is the probability of receiving a prize?

.05

A typical research scenario involving conditional probability involves sampling. For example, suppose that you are evaluating a home care program for the elderly and you want to talk to the program's clientele. You plan to draw a sample of 30% of them, but you can expect that about 20% of the clients will be ineligible for an interview (due to dementia, for example) so you remove them from the sample. What is the probability that any given client will end up in the final sample?

.24

85% of the students at a certain community college have graduated. 35% of those graduates go on to complete bachelor's degrees. What is the probability that a student drawn at random will complete a bachelor's degree?

.2975

A student researcher in psychology has found that after a week, 35% of people who make appointments to complete her memory study do not show up for their appointment, 55% show up and complete the study, and 10% show up, but do not complete the study. What is the probability of showing up for an appointment?

.65

The probability of a teenager in Toronto owning a skateboard is .37, of owning a bicycle is .81, and of owning both is .36. If a Toronto teenager is chosen at random, what is the probability that the teenager owns a skateboard or a bicycle?

.82

A "sure thing" would have a probability equal to

1

How many events of HT (i.e., heads then tails) would you expect to find in the sample space for the probability experiment of tossing two coins sequentially?

1.0

How many outcomes are produced from a trial in a probability experiment?

1.0

In a pet store, there are 6 puppies, 9 kittens, 4 gerbils, and 7 parakeets. If a pet is chosen at random, what is the probability of choosing a puppy or a parakeet?

1/2

According to data from the American Cancer Society, about 1 in 3 women living in the U.S. will have some form of cancer during their lives. If three women are randomly selected, what is the probability that they will all contract cancer at some point during their lives?

1/27

What is the probability of rolling a pair of dice and getting a sum of two?

1/36

What is the probability of the event described in the previous question?

1/4

If you flip a coin, the probability of getting a "head" is 1/2 (or .5). If you flip the coin a second time, what is the probability of getting a "head"?

1/4 or 2/4

If a King is drawn from a deck of cards and placed back in the deck, what then is the probability of drawing the Ace of Spades?

1/52

While under natural conditions there are slightly more boys than girls born, for our purposes let's assume that they are equal in number. Moreover, we know that male gender preference still exists in many parts of the world and is a concern among social demographers. If a woman has three single births in her lifetime, what is the probability that she will have two girls followed by a boy?

1/8

The access code for a security door consists of four digits. Each digit can be any number from 0 through 9. How many access codes are possible?

10000.0

An online survey has boosted participation by offering a prize to every 20th participant who completes a survey. How would the likelihood of receiving a prize be stated as odds?

1:19

What are the odds of rolling a fair die and getting a six?

1:5

What is the probability of rolling a pair of dice and getting a sum of three?

2/36

A day of the week is chosen at random. What is the probability of choosing a weekend day?

2/7

In a statistics class of 13 sophomores, 12 juniors, and 8 seniors, 5 of whom are male sophomores, 6 of whom are female juniors, and 4 of whom are male seniors, what is the probability of randomly selecting a junior or a senior?

20/33 or .61

In the sample space for the probability experiment of rolling a pair of dice, how many outcomes are there?

36.0

Two cards are selected without replacement in sequence from a standard deck. Find the probability the second card is an ace given that the first card was a four.

4/51

Two cards are selected without replacement in sequence from a standard deck. Find the probability the second card is an ace.

4/52

The probability experiment of rolling a single die to see if a number greater than 2 comes up has how many outcomes?

6.0

Given 4 red marbles, 5 blue marbles, and 6 green marbles, what are the odds for picking a green marble?

6:9

A researcher is exploring the notion that there is an economy of scale in raising children. While having one child might add to a family's financial stress, the second or third one might not be as "expensive" since they would already be sharing one roof, could share clothing, etc. The researcher has access to a large community of parents where 15% have one child under 18 in their home, 65% of parents have two children, and 20% of parents have three or more children. Rounded to the nearest whole number, the probability that any given family who is selected has two or more children at home is _____

85%

Which of the following is NOT a probability experiment?

A soccer player scoring a goal

In a probability experiment, an event consists of ___________.

A subset of the sample space

Drawing a king and not drawing a king from a deck of cards are __________.

Complementary events

The multiplication rule can be applied to events that are _______.

Either dependent or independent

Conditional probability refers to the probability that event B will occur given that _______.

Event A has occurred

Identify the true statement: a Events that are not mutually exclusive are also not complementary b Events with shared elements are mutually exclusive c Mutually exclusive events are also not complementary d Dependent events are also not mutually exclusive

Events that are not mutually exclusive are also not complementary

If a die is rolled twice, the outcome of the second trial is not affected by the outcome of the first trial. The events are said to be _______.

Independent

When graphed, the probability distribution of a random variable is likely to appear to be _________.

Normally distributed

The multiplication rule can be thought of as _______.

Probability "and"

The addition rule can be thought of as ________.

Probability "or"

In a coin toss experiment, which of the following expresses the set of all possible outcomes?

S = {H, T}

When applying the addition rule to not mutually exclusive events, why is it necessary to subtract the overlapping elements?

To avoid double counting the shared elements

The fundamental counting principle states that if there are a ways for one event to occur and b ways for another to occur, there are ______ ways for both events to occur.

a x b

Two events, when combined, make up the entire sample space.

complementary

Events can be either simple or ______

compound

The probability of event B given that event A has occurred is known as _________ probability

conditional

if the probability that an event will occur is changed as a result of the occurrence of a previous event, the events are said to be ____

dependent

The researcher in question 4.48 observes that no matter what the survey topic is, 85% of people who are approached at a mall agree to complete a survey. She then concludes that the probability of a person being willing to be surveyed is .85. This represents

empirical probability.

In a probability experiment, the set of all possible outcomes represents the sample space. A subset of those outcomes represents a(n) ____

event

You are interested in the experiences of pregnancy among older women. You begin by asking a sample of 500 women aged 35 and over if they have been pregnant within the past two years. In this study, pregnancy is defined as a(n) ______________

event

Odds represent a ratio of _____ to non-events.

events

If two events are independent, the probability that one will occur is affected (changed) by the occurrence of the other.

false

In the context of a probability experiment, an example of a trial could include buying a Powerball lottery ticket.

false

Making a bet on the Stanley Cup final is an example of a probability experiment.

false

Probability mainly involves hypothetical outcomes and has little application to everyday life.

false

Which of the following pairs of characteristics of people are mutually exclusive?

married & single

A probability experiment involves chance and leads to an observable and _______ result.

measurable

A Venn diagram with overlapping circles can be used to show events that are not _______ (two words).

mutually exclusive

The events "getting a final grade of A in statistics" and "getting a final grade of C in statistics" are _________.

mutually exclusive

Two events that cannot occur at the same time are ________ (two words).

mutually exclusive

Depression and anxiety are not only very common among various social strata, but they often occur simultaneously in an individual, known as comorbidity. Suppose that a sample of young people shows a prevalence of 8% currently suffering from severe depression, 14% from severe anxiety, and 22% suffering from both depression and anxiety. These disorders can be said to be

not mutually exclusive events

Probability can be defined as the likelihood of an event expressed in _________ terms

numerical

Fill in the following series of events: Probability experiment → trial →

outcome

A sample space is a collection of all possible ______ of a probability experiment.

outcomes

A student researcher in psychology has found that after a week, 35% of people who make appointments to complete her memory study do not show up for their appointment, 55% show up and complete the study, and 10% show up, but do not complete the study. What is the complementary event of not showing up?

showing up for the study

In a probability experiment involving the roll of a die, the event "rolling a number greater than five" is a _______ event.

simple

The event of rolling a four on a six-sided die is a ____ event.

simple

A probability estimate based on an educated guess about an outcome is an example of _________ probability

subjective

A researcher believes that the probability of participants willing to be surveyed is higher for surveys about relationships than for surveys about job satisfaction. This an example of_______probability.

subjective

Probability is key to assessing

the likelihood of an event.

Probability is key to assessing and understanding risks.

true

One marble is drawn from a jar containing 4 red, 6 blue, and 7 green marbles. What is the sample space?

{red, blue, green}