Chapter 4

Fill in the blank. ​"At least​ one" is equivalent to​ _______.

"one or More" -Explanation: ​"At least​ one" corresponds to the values​ 1, 2,​ 3, and so on.​ Thus, "At least​ one" is equivalent to​ "one or​ more".

A Social Security number consists of nine digits in a particular​ order, and repetition of digits is allowed. After seeing the last four digits printed on a​ receipt, if you randomly select the other​ digits, what is the probability of getting the correct Social Security number of the person who was given the​ receipt?

.00001

Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 38​% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Complete parts​ (a) and​ (b) below.

.38*.38=.1444

Express the indicated degree of likelihood as a probability value between 0 and 1. Based on a survey of hiring managers who were asked to identify the biggest mistakes that job candidates make during an​ interview, there is a 50-50 chance that they will identify​ "inappropriate attire."

.5

Among 500 randomly selected drivers in the 16 minus 1816−18 age​ bracket, 405 were in a car crash in the last year. If a driver in that age bracket is randomly​ selected, what is the approximate probability that he or she will be in a car crash during the next​ year? Is it unlikely for a driver in that age bracket to be involved in a car crash during a​ year? Is the resulting value high enough to be of concern to those in the 16−18 age​ bracket? Consider an event to be​ "unlikely" if its probability is less than or equal to 0.05.

1) So, P=405/500=.81 2) No 3)Yes

In a small private​ school, 3 students are randomly selected from 16 available students. What is the probability that they are the three youngest​ students?

1/560

11 of the 50 digital video recorders​ (DVRs) in an inventory are known to be defective. What is the probability that a randomly selected item is​ defective?

11/50=.22

If radio station call letters must begin with either K or W and must include either two or three additional​ letters, how many different possibilities are​ there?

36504

When randomly selecting​ adults, let M denote the event of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes. What does P(M|B) represent? Is P(M|B) the same as P(B|M)​?

A What does P(M|B) ​represent? The probability of getting a​ male, given that someone with blue eyes has been selected. B Is P(M|B) the same as P(B|M)​? ​No, because P(B|M) represents the probability of getting someone with blue​ eyes, given that a male has been selected.

Men have XY​ (or YX) chromosomes and women have XX chromosomes.​ X-linked recessive genetic diseases​ (such as juvenile​ retinoschisis) occur when there is a defective X chromosome that occurs without a paired X chromosome that is not defective. Represent a defective X chromosome with lowercase​ x, so a child with the xY or Yx pair of chromosomes will have the disease and a child with XX or XY or YX or xX or Xx will not have the disease. Each parent contributes one of the chromosomes to the child. Complete parts a through d below.

A. If a father has the defective x chromosome and the mother has good XX​ chromosomes, what is the probability that a son will inherit the​ disease? =.0 B. If a father has the defective x chromosome and the mother has good XX​ chromosomes, what is the probability that a daughter will inherit the​ disease? =.0 C. If a mother has one defective x chromosome and one good X chromosome and the father has good XY​ chromosomes, what is the probability that a son will inherit the​ disease? =.5 D. If a mother has one defective x chromosome and one good X chromosome and the father has good XY​ chromosomes, what is the probability that a daughter will inherit the​ disease? =

In a computer instant messaging​ survey, respondents were asked to choose the most fun way to​ flirt, and it found that P(D)=0.7100.710​, where D is directly in person. If someone is randomly​ selected, what does P (D overbar) ​represent, and what is its​ value?

A. P(Doverbar) is the probability of randomly selecting someone who does not choose a direct​in-person encounter as the most fun way to flirt. B. P(Doverbar)= 0.29

There are​ 15,958,866 adults in a region. If a polling organization randomly selects 1235 adults without​ replacement, are the selections independent or​ dependent? If the selections are​ dependent, can they be treated as independent for the purposes of​ calculations?

A. The selections are​ dependent, because the selection is done without replacement. B. ​Yes, because the sample size is less than​ 5% of the population.

The sample space listing the eight simple events that are possible when a couple has three children is​ {bbb, bbg,​ bgb, bgg,​ gbb, gbg,​ ggb, ggg}. After identifying the sample space for a couple having four​ children, find the probability of getting fourfour girlsgirls and nono boysboys.

A. {bbbb,bbbg,bbgb,bgbb,gbbb,bbgg,bgbg,gbbg,bggb,gbgb,ggbb,bggg,gbgg,ggbg,gggb,gggg​} B. Four girls and no boys? P= .0625

Which word is associated with multiplication when computing​ probabilities?

AND -The word​ "and" suggests multiplication and it is associated with the multiplication​ rule, P(A and B)=P(A)* P(B|A)

Fill in the blank. When using the​ _______ always be careful to avoid​ double-counting outcomes.

Addition Rule -Explanation: Errors made when applying the addition rule often involve​ double-counting.

Which of the following is NOT a principle of​ probability? Choose the correct answer below. A. The probability of an impossible event is 0. B. The probability of any event is between 0 and 1 inclusive. C. The probability of an event that is certain to occur is 1. D. All events are equally likely in any probability procedure.

All events are equally likely in any probability procedure. -Explanation: It is not always true that all events are equally likely in any probability procedure.

Use the data in the following​ table, which lists​ drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table.

Are the events of selecting an order from Restaurant A and selecting an accurate order disjoint​ events? The events are not disjoint because it is possible to receive an accurate order from Restaurant A.

Fill in the blank. A​ _______ is any event combining two or more simple events.

Compound Event

Fill in the blank. Events that are​ _______ cannot occur at the same time.

Disjoint -Explanation: Disjoint events are mutually exclusive and cannot occur at the same time.

Fill in the blank. The classical approach to probability requires that the outcomes are​ _______.

Equally likely -Explanation: If the outcomes are not equally​ likely, we cannot use the classical approach to probability.

If A denotes some​ event, what does Search Results Web results Ā denote? If ​P(A)equals=0.0080.008​, what is the value of ​P(Ā)? -If P(A)equals=0.0080.008​, what is the value of ​P(Ā)? -P(Ā)=1-P(A)

Event Ā denotes the complement of event​ A, meaning that Ā consists of all outcomes in which event A does not occur. -0.992

Which of the following values cannot be​ probabilities?

For any event​ A, the probability of A is between 0 and​ 1, inclusive.

In a certain weather forecast, the chance of a thunderstorm weather forecast, the chance of a thunderstorm is stated as 14​%. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.

Here the chance of thunderstorm is 14%. This can be written in Probability value 0 to 1 as 14/100 = 0.14 Thus we can say that Probability of thunderstorm is 0.14

Fill in the blank. Selections made with replacement are considered to be​ _______.

Independent -Explanation: When two selections are made with​ replacement, the first selection does not affect the second selection.​ Therefore, selections made with replacement are independent. Next Question

Fill in the blank. Two events A and B are​ _______ if the occurrence of one does not affect the probability of the occurrence of the other.

Independent -Explanation: Two events A and B are independent if the occurrence of one does not affect the probability of the occurrence of the other.​ (Several events are similarly independent if the occurrence of any does not affect the probabilities of the occurrence of the​ others.) If A and B are not​ independent, they are said to be dependent.

When randomly selecting an​ adult, let B represent the event of randomly selecting someone with type B blood. Write a sentence describing what the rule of complements below is telling us. P(B or B̅)=1

It is certain that the selected adult has type B blood or does not have type B blood.

Which of the following is NOT a requirement of the Permutations​ Rule, nPr=n!/(n-r)! for items that are all​ different?

Order is not taken into account​ (rearrangements of the same items are considered to be the​ same).

When randomly selecting an​ adult, A denotes the event of selecting someone with blue eyes. What do P (A) and Upper P (Ā) ​represent?

P(A) represents the probability of selecting an adult with blue eyes. P(Ā)represents the probability of selecting an adult who does not have blue eyes.

Find the probability that when a couple has six children, at least one of them is a girl. ​(Assume that boys and girls are equally​ likely.)

P(Atleast one of the 6 children is a girl) = 1 - P(No Children is a girl) = 1 - P(All 6 boys) = 1 - (1/2)6 = 63/64

In a test of a​ gender-selection technique, results consisted of 211 baby girls and 208 baby boys. Based on this​ result, what is the probability of a girl born to a couple using this​ technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a​ girl?

P= # of baby girls/Total # of babies=211/419=.504 NO, the technique appears not effective.

Find the indicated complement. A certain group of women has a 0.85​% rate of​ red/green color blindness. If a woman is randomly​ selected, what is the probability that she does not have​ red/green color​ blindness?

P=(1-.0085)= 0.9915

You are certainYou are certain to get a number or a face card when selecting a number or a face card when selecting cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.

P=1

In a certain instant lottery game, the chances of a win instant lottery game, the chances of a win are stated as "5in 23​." Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.

P=5/23=.217

Express the indicated degree of likelihood as a probability value between 0 and 1. When using a computer to randomly generate the last digit of a phone number to be called for a​ survey, there is 1 chance in 10 that the last digit is zero.

Probability=Favorable outcome/# of possible outcomes So, P=1/10=.1

Fill in the blank. A​ _______ variable is a variable that has a single numerical​ value, determined by​ chance, for each outcome of a procedure.

Random

Fill in the blank. P(A)+P(Ā)​= 1 is one way to express the​ _______.

Rule of complementary events

Fill in the blank. The​ _______ for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further.

Sample Space - Explanation: The sample space for a procedure consists of all possible simple events. That​ is, the sample space consists of all outcomes that cannot be broken down any further. Next Question

Assume that 800 births are randomly selected and 761 of the births are girls. Use subjective judgment to describe the number of girls as significantly​ high, significantly​ low, or neither significantly low nor significantly high.

Significantly High

Which of the following is NOT a requirement of the Combinations​ Rule, nCr=n!/r!(n-r)! for items that are all​ different?

That order is taken into account​ (consider rearrangements of the same items to be different​ sequences).

You are certainYou are certain to get a red card when selecting 27a red card when selecting 27 cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.

The Pack of cards has 52 cards out of which 26 are black cards and 26 are red cards. So if a draw of 27 cards are drawn,there will be surely a red card in the collection of 27 cards and so the probability of getting a red rard is 1 The required Probability is 1 ,which is a sure event

Are the events of selecting an order from Restaurant C and selecting an inaccurate order disjoint​ events?

The events are not disjoint because it is possible to receive an inaccurate order from Restaurant C.

Assume that 1400 births are randomly selected and 61 of the births are girls. Use subjective judgment to describe the number of girls as significantly​ high, significantly​ low, or neither significantly low nor significantly high.

The number of girls is significantly low.

What does​ P(B|A) represent?

The probability of event B occurring after it is assumed that event A has already occurred -Explanation: The probability​ P(B|A) represents the probability of event B occurring after it is assumed that event A has already occurred.​ (We can read​ B|A as​ "B given​ A" or as​ "event B occurring after event A has already​ occurred.")

Use the given probability value to determine whether the sample results could easily occur by​ chance, then form a conclusion. A study addressed the issue of whether pregnant women can correctly predict the gender of their baby. Among 104 pregnant​ women, 57 correctly predicted the gender of their baby. If pregnant women have no such​ ability, there is a 0.327 probability of getting such sample results by chance. What do you​ conclude?

The probability shows that the sample results could have easily occurred by chance. It appears that there is not sufficient evidence to conclude that pregnant women can correctly predict the gender of their baby.

Let event A=subject is telling the truth and event B=polygraph test indicates that the subject is lying. Use your own words to translate the notation P(B|A) into a verbal statement.

The probability that the polygraph indicates lying given that the subject is actually telling the truth.

Which of the following is not a requirement of the binomial probability​ distribution?

The trials must be dependent.

If you know the names of the remaining threethree students in the spelling​ bee, what is the probability of randomly selecting an order and getting the order that is used in the spelling​ bee?

There are 6 possible arrangements. ie, 3! = 3 * 2 = 6 Hence, the probability of selecting an order and getting the order = 1/6.

A weather forecasting website indicated that there was a 75​% chance of rain in a certain region. Based on that​ report, which of the following is the most reasonable​ interpretation?

There is a 0.75 probability that it will rain somewhere in the region at some point during the day.

Fill in the blank. A picture of line segments branching out from one starting point illustrating the possible outcomes of a procedure is called a​ _______.

Tree Diagram -Explanation: A tree diagram is a picture of the possible outcomes of a​ procedure, shown as line segments emanating from one starting point. These diagrams are sometimes helpful in determining the number of possible outcomes in a sample​ space, if the number of possibilities is not too large. Next Question

The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a​ student's alarm clock has a 13.6​% daily failure rate. Complete parts​ (a) through​ (d) below.

What is the probability that the​ student's alarm clock will not work on the morning of an important final​ exam? =.136 If the student has two such alarm​ clocks, what is the probability that they both fail on the morning of an important final​ exam?.136*.136=.0185 What is the probability of not being awakened if the student uses three independent alarm​ clocks? .136^3= . 00252 Do the second and third alarm clocks result in greatly improved​ reliability? ​Yes, because total malfunction would not be​ impossible, but it would be unlikely.

A Gallup poll of 1236 adults showed that​ 12% of the respondents believe that it is bad luck to walk under a ladder. Consider the probability that among 30 randomly selected people from the 1236 who were​ polled, there are at least 2 who have that belief. Given that the subjects surveyed were selected without​ replacement, the events are not independent. Can the probability be found by using the binomial probability​ formula? Why or why​ not?

Yes. Although the selections are not​ independent, they can be treated as being independent by applying the​ 5% guideline.

Each of two parents has the genotype brown/blond​, which consists of the pair of alleles that determine hair color​, and each parent contributes one of those alleles to a child. Assume that if the child has at least one brown ​allele, that color will dominate and the​ child's hair color will be brown. a. List the different possible outcomes. Assume that these outcomes are equally likely. b. What is the probability that a child of these parents will have the blond/blond ​genotype? c. What is the probability that the child will have brown hair color​?

a. Brown/Brown, Brown/Blond, Blond/Brown, Blond/Blond b. .25 or 25% c. .75 or 75%

For a certain horse race, the odds in favor of a certain horse finishing in second placehorse race, the odds in favor of a certain horse finishing in second place are given as 19 to 81. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.

first 19+81=100 then P=m/n so P=19/100

As a procedure is repeated again and​ again, the relative frequency of an event tends to approach the actual probability. This is known as​ _______.

the law of the large numbers -Explanation: The law of large numbers tells us that relative frequency approximations tend to get better with more observations.

Complete the following statement. P(A or B) indicates​ _______.

the probability that in a single​ trial, event A​ occurs, event B​ occurs, or they both occur. -Explanation: The probability that in a single​ trial, event A​ occurs, event B​ occurs, or they both​ occur, is P(A or B).