Probability Questions and Answers

Results from a marijuana drug test study showed 143 subjects with positive test results including 24 false positive results. There were 157 negative results, including 3 false negative results. What is the probability that a randomly selected subject did not use marijuana? Round to three decimal places as needed. A. 0.593 B. 0.523 C. 0.477 D. 0.533

Consider the following situation: "A person rolls a four-sided die that has the numbers 1, 2, 3, and 4 on the faces. Then the person spins a spinner that has three regions that are the same size; the colors of the three regions are blue, red, and green. 1. Make a tree diagram to show all of the outcomes for rolling the die and spinning the spinner. 2. How many outcomes are there? List them all.

A modified roulette wheel has 44 slots. One slot is 0, another is 00, and the others are numbered 1 through 42, respectively. You are placing a bet that the outcome is an odd number. (In roulette, 0 and 00 are neither odd nor even.) a. What is your probability of winning? b. What are the actual odds against winning?

Which of the following statements is not true? A. If the probability of an event occurring is 1.5, then it is certain that event will occur. B. If P(A) = 0, then the probability of the complement of A is 1. C. If the probability of an event occurring is 0, then it is impossible for that event to occur. D. Probability can never be a negative value.

A bag contains 3 black balls and 5 white balls. Paul picks a ball at random from the bag and replaces it back in the bag. He mixes the balls in the bag and then picks another ball at random from the bag. Construct a probability tree and calculate the probability that Paul picks a black ball in his second draw. 0.35 0.375 0.41 0.456

An important part of the customer service responsibilities of a cable company is the speed with which service troubles can be repaired. Historically, the data show that the likelihood is .75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, what is the probability that all five will be repaired on the same day? Multiple Choice .0010 .6328 .7627 .2373

In a recent survey of 705 teens, 300 said they have a sister and 383 teens have a brother. One-third of those teens with a sister also have a brother. What is the probability that a teen has a sister or brother? What is the probability that a teen has a sister or no siblings? What is the probability that a teen has a brother or no siblings?

Based on past results found in the Information Please Almanac there is a 0.1919 probability that a baseball World Series will last four games, a 0.2121 probability that it will last five games, a 0.2223 probability that it will last six games, and a 0.3737 probability that it will last seven games. a. Create the probability distribution model.

Suppose that we've decided to test Clara, who works at the Psychic Center, to see if she really has psychic abilities. While talking to her on the phone, we'll thoroughly shuffle a standard deck of 52 cards (which is made up of 13 hearts, 13 spades, 13 diamonds, and 13 clubs) and draw one card at random. We'll ask Clara to name the suit (heart, spade, diamond, or club) of the card we drew. After getting her guess, we'll return the card to the deck, thoroughly shuffle the deck, draw another card, and get her guess for the suit of this second card. We'll repeat this process until we've drawn a total of 15 cards and gotten her suit guesses for each. Assume that Clara is not clairvoyant, that is, assume that she randomly guesses on each card. Answer the following. (If necessary, consult a list of formulas.) (a) Estimate the number of cards in the sample for which Clara correctly guesses the suit by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. (b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places. X 5 2

Listed below are the amounts (dollars) it costs for marriage proposal packages at different baseball stadiums. Find the range, variance, and standard deviation for the given sample data. Include appropriate units in the results. Are there any outliers, and are they likely to have much of an effect on the measures of variation? 39 50 50 55 70 80 90 135 180 216 265 325 500 2000 2750 The range of the sample data is 2711 dollars. (Type an integer or a decimal. Do not round.) The standard deviation of the sample data is (Round to one decimal place as needed.).

A population of values has a normal distribution with μ = 154.9 and σ = 81.7. You intend to draw a random sample of size n = 12. Find the probability that a single randomly selected value is less than 178.5. P(X < 178.5) = Find the probability that a sample of size n = 12 is randomly selected with a mean less than 178.5. P(M < 178.5) = Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z- scores or z-scores rounded to 3 decimal places are accepted.

An experiment is conducted with numbers. Let the S be the sample space. S = {1, 2, 3, 4, 5, 6, 7, 8,9, 10, 11, 12) with events E = {2, 3, 4, 5, 6, 7} F = (5, 6, 7, 8, 9) G = (9, 10, 11, 12) H = (2, 3, 4) Assume each outcome is equally likely. On your paper, list the outcomes in E and G. E and G are E and G have outcomes in common.

Given the following information about events A and B P(A) = 0 P(A AND B) = 0 P(B) = 0.25 Are A and B mutually exclusive, independent, both, or neither? Select the correct answer below: A and B are independent because P(A AND B) = P(A) · P(B). A and B are both independent and mutually exclusive. A and B are mutually exclusive because P(A AND B) = 0. A and B are neither independent nor mutually exclusive.

Pablo randomly picks three marbles from a bag of eight marbles (four red ones, three green ones, and one yellow one). How many outcomes are there in the sample space? How many outcomes in the event that none of the marbles he picks are red?

A real estate agent has 8 master keys to open several new homes. Only 1 master key will open any given house. If 60% of these homes are usually left unlocked, what is the probability that the real estate agent can get into a specific home if the agent selects 3 master keys at random before leaving the office? Options 0.75 0.625 0.7 0.65

A bag contains ten tiles labeled B, C, D, E, F, G, H, I, J, and K. One tile will be randomly picked. What is the probability of picking a vowel? Write your answer as a fraction.

A fair die is rolled 4 times. What is the probability that a 6 is obtained on at least one of the rolls? Round your answer to three decimal places.

A bag contains red and white balls. A pair of balls is selected at random from the bag. The probability that the pair selected will consists one red and one white ball is 6/11. Then the maximum number of balls the bag can contain is 12 17 23 9

A facilities supervisor at a sports stadium wants to rate the condition of the seats at the stadium. Which of the following best describes a stratified sample of seats? The supervisor forms 6 groups of seats based on the dates the seats were last replaced. Then, she selects 9 seats at random from each group. The supervisor forms groups of 9 seats based on the sections the seats are in. Then, she selects all of the seats in 6 randomly chosen groups. All of the seats in the VIP section are easily accessible. So, the supervisor selects the 54 seats in this section.

After the premiere of the new comedy Bumblebee, moviegoers were asked in a quick poll whether they liked the movie. Out of 25 adults, 16 said they liked the movie, whereas out of 100 teenagers, 53 said they liked the movie. Fill in the blanks below to make the most reasonable statement possible. At the movie premiere, ..... moviegoers liked the movie less. That is because ...% disliked the movie, whereas only ....% of the ..... moviegoers disliked the movie.

A coin will be tossed three times, and each toss will be recorded as heads (H) or tails (T). Give the sample space describing all possible outcomes. Then give all of the outcomes for the event that the first toss is heads. Use the format HTH to mean that the first toss is heads, the second is tails, and the third is heads. If there is more than one element in the set, separate them with commas. Sample space: Event that the first toss is heads: {}

At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.14 and the probability that the flight will be delayed is 0.07. The probability that it will not rain and the flight will leave on time is 0.82. What is the probability that it is not raining if the flight leaves on time? Round your answer to the nearest thousandth.

Polychlorinated biphenyl (PCB) is among a group of organic pollutants found in a variety of products, such as coolants, insulating materials, and lubricants in electrical equipment. Disposal of items containing less than 50 parts per million (ppm) PCB is generally not regulated. A certain kind of small capacitor contains PCB with a mean of 47.8 ppm and a standard deviation of 7 ppm. The Environmental Protection Agency takes a random sample of 39 of these small capacitors, planning to regulate the disposal of such capacitors if the sample mean amount of PCB is 49.5 ppm or more. Find the probability that the disposal of such capacitors will be regulated. Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

The mean salary offered to students who are graduating from Coastal State University this year is $24,275, with a standard deviation of $3678. A random sample of 80 Coastal State students graduating this year has been selected. What is the probability that the mean salary offer for these 80 students is $24,250 or more? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

If 2 cards are selected from a standard deck of 52 cards without replacement, find these probabilities. Enter your answers as fractions or as decimals rounded to 3 decimal places. Part 1 of 3 (a) Both are the same suit. P (both are the same suit) = Part 2 of 3 (b) Both are aces. P (both are aces)=

At a gathering consisting of 3 men and 9 women, two door prizes are awarded. Parte: (a) Find the probability that both prizes are won by men. The winning ticket is not replaced. Enter your answer as a fraction or a decimal rounded to 3 decimal places. P(both prizes won by men)

While walking to his stats class, Klutzy Kramer bumped into a table and knocked off a coin and a dle the instructor was planning to use in demonstrating probability. Using a sample space, find the probability that as each landed on the floor, Part 1 of 3 (a) There was a head on the coln and an even number on the die. Express your answer as a reduced fraction. The probability that there was a head on the coin and an even number on the die is Part 2 of 3 (b) There was a tall on the coin and a prime number on the die. Express your answer as a reduced fraction. The probability that there was a tall on the coln and a prime number on the die is Part 3 of 3 (c) There was a head on the coln and a number less than 4 on the dle. Express your answer as a reduced fraction. The probability that there was a head on the coin and a number less than 4 on the die is

Provide an appropriate response. An event is considered unusual if the probability of observing the event is less than 0.025 less than 0.05 greater than 0.95 less than 0.10

From experience, an airline knows that only 85% of the passengers booked for a certain flight actually show up. If 8 passengers are randomly selected, find the probability that at most 5 of them show up. Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places.

Ravi the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Friday there were 3 clients who did Plan A and 8 who did Plan B. On Saturday there were 5 clients who did Plan A and 2 who did Plan B. Ravi trained his Friday clients for a total of 7 hours and his Saturday clients for a total of 6 hours. How long does each of the workout plans last?

In an experiment, a ball is drawn from an urn containing 7 yellow balls and 7 purple balls. If the ball is yellow, three coins are tossed. Otherwise two coins are tossed. How many elements of the sample space will have a yellow ball? How many elements of the sample space are there altogether?

An ice chest contains six cans of apple juice, eight cans of grape juice, four cans of orange juice, and two cans of mango juice. Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting a can of apple juice, then a can of grape juice, then a can of orange juice. The probability of selecting from the ice chest a can of apple juice, then a can of grape juice, then a can of orange juice is .

A rainstorm in Portland, Oregon, wiped out the electricity in 5% of the households in the city. Suppose that a random sample of 70 Portland households is taken after the rainstorm. Answer the following. (a) Estimate the number of households in the sample that lost electricity by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. (b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.

A pet store has 11 puppies, including 3 poodles, 4 terriers, and 4 retrievers. If Rebecka and Aaron, in that order, each select one puppy at random without replacement, find the probability that Aaron selects a retriever, given that Rebecka selects a poodle.

Find the probability that at most 2 heads occured when 5 fair coins are tossed. The probability that at most 2 are heads is

From the sample space S = {1, 2, 3, 4,..., 15) a single number is to be selected at random. Given the following events, find the indicated probability. A: The selected number is even. B: The selected number is a multiple of 4. C: The selected number is a prime number. P(CIA) P(CIA)= (Simplify your answer. Type an integer or a fraction.) .....

A factory received a shipment of 48 hammers, and the vendor who sold the items knows there are 4 hammers in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the hammers in the sample are defective, he will refuse the shipment. For each of the following, give your responses as reduced fractions. If a sample of 4 hammers is selected, find the probability that all in the sample are defective. If a sample of 4 hammers is selected, find the probability that none in the sample are defective.

A desk drawer contains 5 red pens, 6 blue pens, 3 black pens, 24 silver paper clips, and 16 white paper clips. If you select a pen and a paper clip at random, what is the probability that you select a black pen and a white paper clip? Round to the nearest tenth of a percent. A. 9.9% B. 12.12% C. 8.6% D. 11.72%

What is the probability or rolling either an even number or a multiple of 3 when rolling a standard dice? A.1/3 B. 5/6 C. 1/6 D. 2/3

Assume that Jim, Bruce, and Valerie are three of the 34 members of the class, and that three of the class members will be chosen randomly to deliver their reports during the next class meeting. What is the probability that Jim, Bruce, and Valerie are selected in that order? The probability that Jim, Bruce, and Valerie are selected in that order is 1/35,904

A "trifecta" is a particular horse race in which you win by picking the "win," "place," and "show" horses (the first-, second-, and third-place winners), in their proper order. If five horses of equal ability are entered in a trifecta race, and Tracy selects an entry, what is the probability that she will be a winner?

Lisa has one red die and one green die, which she rolls to make up fractions. The green die is the numerator, and the red die is the denominator. Some of the fractions have terminating decimal representations. How many different terminating decimal results can these two dice represent? What is the probability of rolling a fraction with a terminating decimal representation? These two dice can represent different terminating decimal results. (Type a whole number.) The probability of rolling a fraction with a terminating decimal representation is (Type an integer or a simplified fraction.) *****

For the experiment of drawing a single card from a standard 52-card deck, find (a) the probability of the following event, and (b) the odds in favor of the following event. Neither a spade nor a king or queen (a) The probability that the card is neither a spade nor a king or queen is 33/52 (b) The odds, in simplified form, in favor of the event of the card being neither a spade nor a king or queen, are to

A forest contains about 700 trees. You randomly choose 65 trees and find that 30 of them are pine trees. What is the probability that a randomly selected tree will be a pine tree? Is this probability theoretical or experimental? 65/700-9%; experimental 30/65=46%; expermental 30/700-4%; theoretical

A box has 19 candies in it: 3 are peppermint, 5 are butterscotch, and 11 are taffy. Reuben wants to select two candies to eat for dessert. The first candy will be selected at random, and then the second candy will be selected at random from the remaining candies. What is the probability that the two candies selected are peppermint?

Luka and Janie are playing a coin toss game. If the coin lands heads up, Luka earns a point; otherwise, Janie earns a point. The first player to reach 22 points wins the game. If 21 of the first 41 tosses have been heads, what is the probability that Janie wins the game?

The digits 3, 4, 5, 6, and 7 are randomly arranged to form a five-digit number. Complete parts (a) and (b) below. (a) Find the probability that the number is odd. The probability that the number is odd is (Type an integer or a simplified fraction.) -

Two integers are randomly selected from the set {1, 2, 3, 4, 5, 6, 7, 8, 9) and are added together. Find the probability that their sum is 12 if they are selected (a) with replacement, (b) without replacement.

Let A and B be two events. Suppose that P (A)=0.52 and P (B)=0.13. (a) Find P(AorB), given that A and B are mutually exclusive. (b) Find P(AorB), given that A and B are independent.

You draw a single card from a deck of 52 playing cards. (Reminder: There are four suits including clubs, spades, hearts and diamonds. Each suit has 13 cards with numbers Ace through ten and face cards of Jack, Queen, and King.) Find: a) P(Ace) b) P(Ace of spades it is a black card) c) P(Ace of spades the Queens are missing from the deck)