Probability Questions and Answers

A grocery store manager took inventory of all the fruit to decide what needed to be donated. Of the twelve pieces of fruit deemed overripe, four were apples. If the manager randomly selected three of the overripe pieces for the first donation package, what is the probability that all of them are apples?

Consider the data set below. 70, 120, 110, 101, 88, 83, 95, 98, 107, 100 If the population mean is 100, what is the t-value for the given data set? -0.13 -0.38 -0.62 -2.80

Suppose that on a true/false exam you have no idea at all about the answers to three questions. You choose answers randomly and therefore have a 50-50 chance of being correct on any one question. Let CCW indicate that you were correct on the first two questions and wrong on the third, let WCW indicate that you were wrong on the first and third and correct on the second, and so forth. Then S = {CCC, CCW, CWC, WCC, CWW, WCW, WWC, WwW) is the sample space of all possible sequences of correct and incorrect responses on your part. (1) Let E₁ be the event that exactly one answer is correct. (i) Write E₁ as a set in the set-roster notation: E₁ = { (ii) What is the probability of E₁? (2) Let E₂ be the event that at least two answers are correct. (i) Write E₂ as a set in set-roster notation: E₂ = { (ii) What is the probability of E2? }

A student picks a random letter from the word "cat" and a random letter from the word "meow." Express answers that are not whole numbers as fractions. a. How many outcomes are in the sample space? b. What is the probability that a "C" is chosen? c. What is the probability that a "W" is chosen? d. What is the probability that a "C" and "W" are chosen?

Janelle requested one statistics book from two different libraries of her neighborhood. There is 52% chance that the book is available in the first library and there is 25% chance of its availability in the second library. The probability that Janelle can check out the statistics book from the second library and not from the first library is The probability that the book is not available for checkout at either of the libraries is

At a busy street corner, one of every hundred jaywalkers will be hit when they cross. What is the probability of a jaywalker not being hit if he makes a round trip daily for thirty days? (0.01)^30 (0.99)^30 (0.9801)^30

A certain city has one chance in two of receiving rain on June 1, one chance in five of receiving rain on July 1, and two chances in three of receiving rain on August 1. What is the probability that the city will receive rain on none of these days? 2/15 2/5 14/15

Twenty students belong to a summer baseball team, Included Sam and Jose. Each day at practice, two are randomly chosen to go fill the team thermos with Ice water. Assuming all players are present, what are the chances Sam and Jose are chosen at five practices in a row? (1/190)^5 (1/380)^5 (15,504)^2 (1/190)^2

The probability for success of an event is P(A), and the probability of success of a second event is P(B). What is the probability of both events occurring, in that order? P(A + B) P(A). P(B) P(A) + P(B) P(A x B)

One bag contains three white marbles and five black marbles, and a second bag contains four white marbles and six black marbles. A person draws one marble from each bag. Find the probability that both marbles are of the same color. 21/40 1/2 3/14

The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 117 millimeters of mercury (mmHg) and standard deviation of 22. Someone qualifies as having Stage 2 high blood pressure if their systolic blood pressure is 160 or higher. Stage 1 high BP is specified as systolic BP between 140 and 160. Give your answers rounded to 4 decimal places. a. What is the probability that an adult in the USA has stage 2 high blood pressure? b. What is the probability that an adult in the USA has stage 1 high blood pressure?

A marble is drawn from a box containing 4 yellow, 5 white, and 19 blue marbles. Find the odds in favor of not drawing a white marble. In reduced form, the odds in favor of not drawing a white marble are (Simplify your answers.) ***

A job applicant estimates that his chance of passing a qualifying examination is 2/3, and his chance of being appointed if he does pass is 1/4. What is the probability that he will receive the job? 1/6 1/4 11/12

There are five different fish, each of a different species, in a tank that needs to be cleaned. What is the probability that the first two scooped out are a goldfish and a guppy, in that order, assuming both are included among the species in the tank? 1/20 1/60 1/12 1/30

In a small town parade, the band always goes first and the horses go last. In between are five floats, labeled A, B, C, D, and E. Assuming equal probability for all float positions, what is the probability that the lineup will be band, D, C, A, E, B, horses? 1/120 1/5,040 1/5 1/21

A class of 160 students contains 40 honor students, 60 athletes, and 80 who are neither athletes nor honor students. From the entire group a student is chosen at random. What is the probability that the student chosen is an honor student given that he is an athlete? 1/8 1/3 1/2

Nine new employees, two of whom are married to each other, are to be assigned nine desks that are lined up in a row. If the assignment of employees to desks is made randomly, what is the probability that the married couple will have adjacent desks? (Round your answer to the nearest tenth of a percent.) The probability that the couple has adjacent desks is What is the probability that the married couple will have nonadjacent desks? (Round your answer to the nearest tenth of a percent.) The probability that the couple has nonadjacent desks is

Compute probabilities of each outcome by dividing the frequency of each row by ten. This is the empirical probability of each outcome. Compute theoretical probability for each row, using combinations. Compare the results. Were your probabilities the same or not? If they were the same, will they always happen? Explain why. If they were different, will that always happen? Explain why.

On a particular day, the mean price of gasoline was $3.63 a gallon with a standard deviation of $0.20 a gallon. What is the probability that a gas station has a price between $3.43 and $3.63 a gallon? Use the 68-95-99.7 normal distribution curve.

A geologist has ten rock samples in a bag and is going to use eight for class. What is the probability that the first three pulled out will be hematite, bauxite, and coal in that order, assuming all three are among the rock samples? 1/720 1/240 1/2,160 1/1,680

Two balls are to be selected with replacement from a hat with one red, one blue, one yellow, and one green ball. Determine the probability of selecting at least one green ball. Assume each ball is identical except color so that each is equally likely to be selected. 1/16 1/4 3/8 7/16

You have six flower vases that you would like to display on a shelf, but only three can fit. You would like to have the white vase placed in the middle. If you randomly select the three vases, what is the probability of getting a white vase in the middle? 1/2 1/3 1/4 1/6

An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events. Event A: The sum is greater than 5. Event B: The sum is an odd number.

A certain class of 160 students has 40 honor students and 60 athletes. Eighty students in the class do not participate in sports and are not honor students. If a student is selected at random to represent the class, what is the probability that he is both an honor student and an athlete? 1/8 1/2 5/8

Which of the following predictions can be calculated using a binomial distribution? a.Whether a baseball player will hit a home run during a five-game series b. The number of product samples that will be tested before a defective one is found c.Both of the above d. None of the above

If a child's knowledge of the alphabet is limited to the letters a, b, c, i, and e, and if the child writes two letters at random (assume the child may write the same letter twice), what is the probability that one is a vowel and the other is a consonant? 6/25 12/25 4/5

The sale of sports cars in the United States during one year was 550,000. Two hundred five thousand cars had six cylinders and the rest had four cylinders. What is the probability that the next sports car you see in the United States will have six cylinders? 69/110 41/110 401/1,100

You are given that the probability of event A is 0.232, the probability of event B is 0.404, and the probability of either event A or event B is 0.5664. Enter three correct decimal places in your response. That is, calculate the answer to at least four decimals and report only the first three. For example, if the calculated answer is 0.123456 enter 0.123. What is the probability of both event A and event B? What is the probability that event A doesn't occur?

You are setting up a trophy display with twelve out of fifteen trophies for your school. Any trophy can fit anywhere in the display, but the principal has instructed you to put the four first place trophies in four specific spots. What is the probability that placing the trophies at random would work? 1/32,760 1/1,880 1/35,640 1/98,280

There are ten kittens, each a different breed, available for adoption at an animal shelter. Assume the probabilities of kittens being adopted are equal. What is the probability that the first two kittens adopted are the American Short Hair and the Maine Coon? 1/72 1/90 1/6 1/45

Your family goes to the beach every year for your birthday when weather permits. Your birthday is July 10. If the probability of rain on July 10 is 0.35, what is the probability that it rains on your birthday for two consecutive years? 0.1225 0.2300 0.4600 0.0121

The tickets in a box are numbered from 1 to 20 inclusive. If a ticket is drawn at random and replaced, and then a second ticket is drawn at random, what is the probability that the sum of their numbers is even? 1/2 1/4 1/5

A spinner has five equal parts each painted with red, blue, orange, yellow, and green, respectively. Shelly spins the spinner twice. What is the probability of getting red on both spins?

In a group of 100 persons, 85 had Rh positive blood (Rh factor present, Rh+), 45 had Type O blood, and 38 had both Type O and Rh positive blood. If one person had been selected at random from the group, what would the probability be: 1. that his blood type was Type O and Rh+? 2. that his blood type was not O? 3. that his blood type was Rh-? 4. that his blood type was Type O and Rh-? 5. that his blood type was Rh+? 6. that his blood type was not Type O or else was Rh+? 11/20 17/20 93/100 19/50 3/20 7/100

A golf ball is selected at random from a golf bag. If the golf bag contains 8 brown balls, 6 orange balls, and 4 green balls, find the probability of the following event. The golf ball is brown or orange.

A researcher wants to find out which dandruff shampoo works better. He takes 100 volunteers and randomly gives half of them brand A and the other half brand B. 17% of people using Brand A report improvement in their dandruff and 20% of people using Brand B report improvement in their dandruff. 20% 17% 100% 17% and 20%

Every morning an office manager provides a box of twelve jelly doughnuts for the staff. Each doughnut has a different flavored filling. Every day you randomly pick two doughnuts and you pick from the full box. If you eat two doughnuts every day, what is the probability that you will eat the lemon and the cherry doughnuts for three days in a row?

From 6 cards bearing the letters a, b, c, d, e, and f, two cards are drawn. Find the probability that at least one of the cards drawn bears a vowel. Note: (a, b) and (b, a) are considered to be different elements in the sample space. 2/15 3/5 5/9

Examine the life table on the previous page, and look at the age range of 85-86. Out of 100,000 randomly selected people, 38,565 survive to age 85, and the probability of dying between age 85 and age 86 is 0.090346. Likewise, 35,081 people survive to age 86, and the probably of dying between age 86 and age 87 is 0.099341. This means that: The probability of surviving to age 85 is The probability of surviving to age 86 is The probability of surviving to age 86, given that you've survived to age 85, is 1-0.090346 =

The probability that a randomly chosen American adult gets less than an average of 7 hours of sleep a night is 0.352. The probability that a randomly chosen American adult gets less than an average of 7 hours of sleep a night AND has at least one child under the age of three is 0.195. What is the probability that an American adult has at least one child under the age of three given that they get less than an average of 7 hours of sleep? 0.069 0.157 0.647 0.554

The average repair cost of a microwave oven is $55, with a standard deviation of $8. The costs are normally distributed. If 12 (sample) ovens are repaired, find the probability that the mean of the repair bills will be greater than $60. .4985 .9845 .243 .015

A bag of marbles has four red, six green, and five blue marbles. A person grabs three marbles from the bag. Find the probability that exactly two blue marbles are drawn. 10/455 45/455 90/455 100/455

Tasha is in the science club. There are 21 students in the club. Two of them will be picked at random to attend an awards banquet. What is the probability that Tasha will not be randomly chosen to attend the banquet?

A coin is flipped twice and a number cube is rolled once. What is the probability of observing heads, then tails, and rolling an even number? Assume that each option is equally likely to be chosen.

Find the number of possible outcomes in the sample space. A pizza stand offers both hand-tossed and pan pizza. Each pizza can either be a white pizza with no sauce or a red pizza with sauce. O 0 O 9 O 4 O 5 O 3

tis estimated that there are 32 deaths for every 10 million people who use airplanes. A company that sells fight insurance provides $100,000 in case of death in a plane crash. A policy can be purchased for $1. Calculate the expected and thereby determine how much the insurance company can make over the long run for each policy that it sells

According to a poll about phone use, 25% of all U.S. households are "wireless only," meaning they do not have a land line. In a random sample of 15 households, what is the expected number of households that are wireless only? 4 3.75 3 0.25

A statistics teacher organizes a drawing each semester. During this raffle, she writes the names of each of her 100 students on slips of paper, each with an equal chance of winning. After drawing each name, the teacher replaces it in the bin, meaning that a student could win more than once. The first name she draws will get 20 points extra credit; the second name she draws will get 10 points extra credit; the third name she draws will get 5 points extra credit. The students who don't win any extra points all lose 1 point from their final grade. Let X be the average points won or lost by students. All 100 students choose to enter. What is E(X)? -0.62 -0.97 0.97 1

For a certain candy, 20% of the pieces are yellow, 5% are red, 15% are blue, 5% are green, and the rest are brown. a) If you pick a piece at random, what is the probability that it is brown? it is yellow or blue? it is not green? it is striped? b) Assume you have an infinite supply of these candy pieces from which to draw. If you pick three pieces in a row, what is the probability that they a) The probability that it is brown is .63. (Round to three decimal places as needed.) The probability that it is yellow or blue is .35. (Round to three decimal places as needed.) The probability that it is not green is .95. (Round to three decimal places as needed.) The probability that it is striped is 0. (Round to three decimal places as needed. b) The probability of picking three brown candies is .166. (Round to three decimal places as needed.) The probability of the third one being the first red one is .045. (Round to three decimal places as needed.) The probability that none are yellow is (Round to three decimal places as needed.)

You are earning a salary of $40,000 a year and your position is steady. However, you have an opportunity to start your own business. You have done the research and it has shown that starting your own company gives you a 20% chance of earning $200,000 a year, a 40% chance of earning $100,000 a year, and a 40% chance of complete failure. What is the expected value of giving up your $40,000 salary and starting your own business? $80,000 $40,000 $10,000 $500,000