# Probability Questions and Answers

Statistics

ProbabilityInsurance: An insurance company sells a 1-year term life insurance policy to an 77-year-old woman. The woman pays a premium of $1200. If she dies within 1 year, the company will pay $26,000 to her beneficiary. According to the U.S. Centers for Disease Control and Prevention, the probability that an 77-year-old woman will be alive 1 year later is 0.9561. Let X be the profit made by the insurance company.

Statistics

ProbabilityDo you carpool? Let X represent the number of occupants in a randomly chosen car on a certain stretch of highway during morning commute hours. A survey of cars showed that the probability distribution of X is as follows.
x 1 2 3 4 5
P(x) 0.64 0.11 0.09 0.02 0.14

Statistics

Probability(e) A computer system requires that passwords contain at least one digit. What is the probability that a valid password will be generated? Round your answer to four decimal places.
The probability that a valid password will be generated is

Statistics

ProbabilityIn a certain country, the true probability of a baby being a boy is 0.533. Among the next six randomly selected births in the country, what is the probability that at least one of them is a girl?

Statistics

ProbabilityBased on a survey, assume that 29% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when five consumers are randomly selected, exactly two of them are comfortable with delivery by drones. Identify the values of n, x, p, and q.
The value of n is.
The value of x is
The value of p is
The value of q is.

Statistics

ProbabilityFor a certain instant lottery game, the odds in favor of a win are given as 23 to 77. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
The probability is

Statistics

ProbabilityChoosing officers: A committee consists of eight women and ten men. Four committee members will be chosen as officers.
How many different choices are possible?
There are different possible choices.
How many different choices are possible if all the officers are to be women?
There are different choices possible if all the officers are to be women.
How many different choices are possible if all the officers are to be men?
There are different choices possible if all the officers are to be men.

Statistics

ProbabilityWhen testing for current in a cable with seven color-coded wires, the author used a meter to test five wires at a time. How many different tests are required for every possible pairing of five wires?
The number of tests required is.

Statistics

ProbabilityWhen testing for current in a cable with eleven color-coded wires, the author used a meter to test three wires at a time. How many different tests are required for every possible pairing of three wires?

Statistics

ProbabilityGoogle it: According to a report of the Nielsen Company, 60% of internet searches used the Google search engine. Assume that a sample of 23 searches is studied. Round the answers to at least four decimal places.
(a) What is the probability that exactly 18 of them used Google?
The probability that exactly 18 of them used Google is

Statistics

ProbabilityCar inspection: Of all the registered automobiles in Colorado, 5% fail the state emissions test. Twelve automobiles are selected at random to undergo emissions test. Round the answers to at least four decimal places.
(a) Find the probability that exactly three of them fail the test.
The probability that exactly three of them fail the test is
(b) Find the probability that fewer than three of them fail the test.
The probability that fewer than three of them fail the test is
(c) Find the probability that more than two of them fail the test.
The probability that more than two of them fail the test is

Statistics

ProbabilityEach of two parents has the genotype green/brown, which consists of the pair of alleles that determine
eye color, and each parent contributes one of those alleles to a child. Assume that if the child has at least one green allele, that color will dominate and the child's eye color will be green.
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 brown/brown genotype?
c. What is the probability that the child will have green eye color?
***
a. List the possible outcomes.
A. green/green, green/brown, and brown/brown
B. green/brown and brown/green
C. green/green, green/brown, brown/green, and brown/brown
D. green/green and brown/brown
b. The probability that a child of these parents will have the brown/brown genotype is 0.25
(Round to two decimal places as needed.)
c. The probability that the child will have green eye color is.
(Round to two decimal places as needed.)

Statistics

ProbabilityBlood types: The blood type O negative is called the "universal donor" type, because it is the only blood type that may safely be transfused into any person. Therefore, when someone needs a transfusion in an emergency and their blood type cannot be determined, they are given type O negative blood. For this reason, donors with this blood type are crucial to blood banks. Unfortunately, this blood type is fairly rare; according to the Red Cross, only 5% of U.S. residents have type O negative blood. Assume that a blood bank has recruited 20 donors. Round the answers to at least four decimal places.
(a) What is the probability that two or more of them have type O negative blood? The probability that two or more of them have type O negative blood is 0.2642
(b) What is the probability that fewer than four of them have type O negative blood? The probability that fewer than four of them have type O negative blood is 0.9841
(c) Would it be unusual if none of the donors had type O negative blood? Use a cutoff of 0.05.

Statistics

Probability(a) Make the logarithmic transformations x' log (x) and y'= log (y). Then make a scatter plot of the (x, y) values. Does a linear equation seem to be a good fit to this plot?
The transformed data does not fit a straight line well. The data seem to explode as x decreases.
The transformed data does not fit a straight line well. The data seem to explode as x increases.
The transformed data fit a straight line well.
The transformed data does not fit a straight line well. The data seem to have a parabolic shape.
(b) Use the (x, y) data points and a calculator with regression keys to find the least-squares equation y'= a + bx'. What is the correlation coefficient? (Use 4 decimal places.)
y' =
r=
(c) Use the results of part (b) to find estimates for a and ß in the power law y = ax. Write the power equation for the relationship between steam pressure and sheer strength of boiler plate
steel. (Use 4 decimal places.)
R=
B =
ŷ=
11

Statistics

ProbabilityThe patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and standard deviation of 2.1 days. Use your graphing calculator to answer the following questions.
Write your answers in percent form. Round your answers to the nearest tenth of a percent.
a) What is the probability of spending less than 8 days in recovery?
b) What is the probability of spending more than 5 days in recovery?
c) What is the probability of spending between 5 days and 8 days in recovery?

Statistics

ProbabilitySara draws the 10 of hearts from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card.
a. Determine the probability that the second card is another 10.
P(10 | 10 of hearts) =
b. Determine the probability that the second card is another heart.
P(heart |10 of hearts) =
c. Determine the probability that the second card is a club.
P(club |10 of hearts) =
d. Determine the probability that the second card is a 8
P(8 | 10 of hearts) =

Statistics

ProbabilityIn a class of students, the following data table summarizes how many students have a brother or a sister. What is the probability that a student has a brother given that they do not have a sister?
Has a brother Does not have a brother
Has a sister 3 14
Does not have a sister 7 2

Statistics

ProbabilityA committee consists of eight women and ten men. Four committee members will be chosen as officers.

Statistics

Probability39.8% of consumers believe that cash will be obsolete in the next 20 years. Assume that 7 consumers are randomly selected. Find the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years.

Statistics

ProbabilityWhen 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(MIB) represent? Is P(MIB) the same as P(BIM)?
What does P(MIB) represent?
A. The probability of getting a male or getting someone with blue eyes.
B. The probability of getting a male and getting someone with blue eyes.
C. The probability of getting a male, given that someone with blue eyes has been selected.
D. The probability of getting someone with blue eyes, given that a male has been selected.

Statistics

ProbabilityA classic counting problem is to determine the number of different ways that the letters of "occurrence" can be arranged. Find that number. If the letters are mixed up in a random sequence, what is the probability that the letters will be in alphabetical order?

Statistics

ProbabilityIn a certain study, the chances of encountering a car crash on the road are stated as "7 in 20." Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.

Statistics

ProbabilityMultiple-choice questions each have four possible answers (a, b, c, d), one of which is correct. Assume that you guess the answers to three such questions.
a. Use the multiplication rule to find P(CWW), where C denotes a correct answer and W denotes a wrong answer.
P(CWW) =
b. Beginning with CWW, make a complete list of the different possible arrangements of one correct answer and two wrong answers, then find the probability for each entry in the list.
P(CWW)- see above
P(WWC) =
P(WCW) =

Statistics

ProbabilityDetermine whether the value is a discrete random variable, continuous random variable, or not a random variable.
a. The amount of snowfall in December in City A
b. The number of fish caught during a fishing tournament
c. The eye color of people on commercial aircraft flights
d. The distance a baseball travels in the air after being hit
e. The amount of rain in City B during April
f. The weight of a T-bone steak
***
a. Is the amount of snowfall in December in City A a discrete random variable, a continuous random variable, or not a
random variable?
A. It is a continuous random variable.
B. It is a discrete random variable.
C. It is not a random variable.

Statistics

ProbabilityJared buys a bag of cookies that contains 6 chocolate chip cookies, 6 peanut butter cookies, 6 sugar cookies and 6 oatmeal raisin cookies. What is the probability that Jared randomly selects a sugar cookie from the bag, eats it, then randomly selects another sugar cookie? Express your answer as a reduced fraction.

Statistics

ProbabilityA thief steals an ATM card and must randomly guess the correct four-digit pin code from a 9-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?
The number of possible codes is
(Type an integer or fraction. Simplify your answer.)
The probability that the correct code is given on the first try is
(Type an integer or fraction. Simplify your answer.)

Statistics

ProbabilityHow many different ways can the letters of "attract" be arranged?
The number of different ways that the letters of "attract" can be arranged is.

Statistics

ProbabilityBased on a survey, assume that 41% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when four consumers are randomly selected, exactly two of them are comfortable with delivery by drones. Identify the values of n, x, p, and q.

Statistics

ProbabilityAssume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 22 couples. Complete parts (a) through (c) below.
a. Find the mean and the standard deviation for the numbers of girls in groups of 22 births.
The value of the mean is µ = 11.
(Type an integer or a decimal. Do not round.)
The value of the standard deviation is o = 2.3.
(Round to one decimal place as needed.)
b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high

Statistics

ProbabilityYou are certain to get 3 jacks when selecting 51 cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.

Statistics

ProbabilityA research center poll showed that 77% of people believe that it is morally wrong to not report all income on tax returns What is the probability that someone does not have this belief?

Statistics

ProbabilityFor a certain horse race, the odds in favor of a certain horse finishing in second place are given as 7 to 93. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.

Statistics

ProbabilityA research center poll showed that 78% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief?

Statistics

ProbabilityWhich word is associated with multiplication when computing probabilities?
Choose the correct answer below.
Disjoint
And
Or
Not

Statistics

ProbabilityLet A = the event of getting at least one defective calculator when four are randomly selected with replacement from a batch. Write a statement describing event Ā.
Choose the correct answer below.
A. The event of getting no defects among the 4 calculators.
B. The event of getting 4 defects among the 4 calculators.
C. The event of getting at least 1 defect among the 4 calculators.
D. The event f getting more than 1 defect among the 4 calculators.

Statistics

ProbabilityLet 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(BIA) into a verbal statement.
Choose the correct option below.
A. The probability that the polygraph indicates lying given that the subject is actually lying.
B. The probability that the polygraph indicates lying given that the subject is actually telling the truth.
C. The probability that the polygraph indicates truthfulness given that the subject is actually telling the truth.
D. The probability that the polygraph indicates truthfulness given that the subject is actually lying.

Statistics

ProbabilityAssume that boys and girls are equally likely. Find the probability that when a couple has three children, there is exactly 1 boy.

Statistics

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

Statistics

ProbabilityFor a standard normal distribution, find:
A(z > -2.01)
Round to 4 decimal places.

Statistics

ProbabilityIn a particular survey of internet users, 3663 respondents say that they use social networking sites and 1330 respondents say that they do not use social networking sites. What is the probability that a randomly selected person uses a social networking site? Does that result suggest that it is likely (with a probability of 0.5 or greater) for someone to use social networking sites?

Statistics

ProbabilityLet A denote the event of placing a $1 straight bet on a certain lottery and winning. Suppose that, for this particular lottery, there are 5,400 different ways that you can select the four digits (with repetition allowed) in this lottery, and only one of those four-digit numbers will be the winner. What is the value of P(A)? What is the value of P(A)? What is the value of P(A)?

Statistics

ProbabilityFind 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.)

Statistics

ProbabilityFor 100 births, P(exactly 55 girls) = 0.0485 and P(55 or more girls) = 0.184. Is 55 girls in 100 births a significantly high number of girls? Which probability is relevant to answering that question? Consider a number of girls to be significantly high if the appropriate probability is 0.05 or less.

Statistics

ProbabilityYou are certain to get 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.

Statistics

ProbabilityAccording to a report of the Nielsen Company, 60% of internet searches used the Google search engine. Assume that a sample of 23 searches is studied. Round the answers to at least four decimal places.

Statistics

ProbabilitySuppose the mean IQ score of people in a certain country is 102. Suppose the director of a college obtains a simple random sample of 43 students from that country
and finds the mean IQ is 105.6 with a standard deviation of 13.1. Complete parts (a) through (d) below. conclusion for the test.
Explain what the director is testing. Choose the correct answer below.
A.The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually equal to 103.
B. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually greater than 103.
C. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually not greater than 103.
D.The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually not equal to 103.
Find the test statistic for this hypothesis test.
(Round to two decimal places as needed.)
Find the P-value for this hypothesis test.
(Round to three decimal places as needed.)

Statistics

ProbabilityThe data in the accompanying table represent the number of corn plants in randomly sampled rows (a 17-foot by 5-inch strip) for various types of plots. An agricultural researcher wants to know whether the mean numbers of plants for each plot type are equal. Complete parts (a) through (e) below.
Click the icon to view the data table.
Click the icon to view the table of critical values for the correlation coefficient.
(a) Write the null and alternative hypotheses. Choose the correct answer below.
A. Ho: Hsludge = Hspring="no till and H₁: at least one of the means is different
B. Ho: at least one of the means is different and H₁: Hsludge = Hspring Hno till
C. Ho: Hsludge = spring and H₁: the means are different
D. Ho: Hsludge = spring = Hno till and H₁ Hsludge Hspring <Hno till
(b) State the requirements that must be satisfied to use the one-way ANOVA procedure. Select all that apply.
A. The k samples must be independent of each other.
B. There must be k simple random samples, one from each of k populations.
C. There must be k simple random samples, each from the same population.
D. The populations must be normally distributed.

Statistics

ProbabilityA sample of 250 internet users was selected. Find the complements of the following events.

Statistics

ProbabilitySick computers: Let V be the event that a computer contains a virus, and let W be the event that a computer contains a worm. Suppose
P(V)=0.31, P (W)=0.4, P (V and W) = 0.07.
(a) Find the probability that the computer contains either a virus or a worm or both.
(b) Find the probability that the computer does not contain a worm.