Probability Questions and Answers

If a person spins a six-space spinner and then flips a coin, describe the sample space of possible outcomes using 1, 2, 3, 4, 5, 6 for the spinner outcomes and H, T for the coin outcomes. The sample space is S={ (Use a comma to separate answers as needed.)

Suppose you toss a coin 100 times and get 51 heads and 49 tails. Based on these results, what is the probability that the next flip results in a head? The probability that the next flip results in a head is approximately

Take a guess: A student takes a multiple-choice test that has 11 questions. Each question has four choices. The student guesses randomly at each answer. Let X be the number of questions answered correctly. Round the answers to at least four decimal places. (a) P (4) = (b) P (More than 3) =

In Hawaii, the rate of motor vehicle theft is 503 thefts per 100,000 vehicles. A large parking structure in Honolulu has issued 554 parking permits. (a) What is the probability that none of the vehicles with a permit will eventually be stolen? (Round λ to 1 decimal place. Use 4 decimal places for your answer.) (b) What is the probability that at least one of the vehicles with a permit will eventually be stolen? (Use 4 decimal places.) (c) What is the probability that nine or more vehicles with a permit will eventually be stolen? (Use 4 decimal places.)

A binomial experiment has the given number of trials n and the given success probability p. n=15, p=0.2 (a) Determine the probability P(7). Round the answer to at least four decimal places. P(7)= (b) Find the mean. Round the answer to two decimal places. The mean is (c) Find the variance and standard deviation. Round the variance to two decimal places and standard deviation to at least three decimal places. The variance is The standard deviation is

In western Kansas, the summer density of hailstorms is estimated at about 2.2 storms per 5 square miles. In most cases, a hailstorm damages only a relatively small area in a square insurance company has insured a tract of 10 square miles of Kansas wheat land against hail damage. Let r be a random variable that represents the number of hailstorms this summer in the 10-square-mile tract. (a) Explain why a Poisson probability distribution is appropriate for r. Hail storms in western Kansas are a common occurrence. It is reasonable to assume the events are independent. Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are dependent. Hail storms in western Kansas are a common occurrence. It is reasonable to assume the events are dependent. Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are independent. What is λ for the 10-square-mile tract of land? Round λ to the nearest tenth so that you can use Table 4 of Appendix II for Poisson probabilities. (b) If there already have been two hailstorms this summer, what is the probability that there will be a total of four or more hailstorms in this tract of land? Compute P(r24|r≥ 2). (Round your answer to four decimal places.) (c) If there already have been three hailstorms this summer, what is the probability that there will be a total of fewer than six hailstorms? Compute P(r< 6 | r≥ 3). (Round your answer to four decimal places.)

The one-time fling! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party, and then returned the purchase? This is called a one-time fling. About 5% of all adults deliberately do a one-time fling and feel no quilt about it! In a group of eight adult friends, what is the probability of the following? (Round your answers to three decimal places.) (a) no one has done a one-time fling (b) at least one person has done a one-time fling (c) no more than two people have done a one-time fling.

Approximately 7.8% of all (untreated) Jonathan apples had bitter pit in a study conducted by the botanists Ratkowsky and Martin. (Bitter pit is a disease of apples resulting in a soggy ore, which can be caused either by overwatering the apple tree or by a calcium deficiency in the soil.) Let n be a random variable that represents the first Jonathan apple chosen at random that has bitter pit. (a) Write out a formula for the probability distribution of the random variable n. (Use p and n in your answer.) P(n)= (b) Find the probabilities that n = 3, n = 5, and n 12. (Use 3 decimal places.) P(3) P(5) P(12) (c) Find the probability that n 2 5. (Use 3 decimal places.) (d) What is the expected number of apples that must be examined to find the first one with bitter pit? Hint: Use for the geometric distribution and round.

Statistics released by a reputable traffic safety organization show that on an average weekend night, 1 out of every 10 drivers on the road is drunk. If 400 drivers are randomly checked next Saturday night, what is the probability that the number of drunk drivers will be (a) less than 34? (b) more than 52? (c) at least 43 but less than 55?

Work with others and get as much help as you like, but you must submit your own copy of your own work. Any or all problems may be graded. You must show your work for full credit, even if it only means telling us what calculator function(s) you used: providing a final answer and no work is not enough. 1. a. If you flip a coin 10 times, and it shows heads exactly 5 times, does this mean the coin must be fair? Explain. b. If you flip a coin 100 times and it shows heads exactly 50 times, does this mean the coin must be fair? Explain. c. Which case above (a or b) gives you more confidence that the coin is actually fair? d. If you flip a coin 100 times, what is the probability that the coin will show heads exactly 50 times? e. Do your responses to c. and d. above conflict with each other? Explain.

A common practice of airline companies is to sell more tickets for a particular flight than there are seats on the plane, because customers who buy tickets do not always show up for the flight. Suppose that the percentage of no-shows at flight time is 2%. For a particular flight with 195 seats, a total of 200 tickets were sold. What is the probability that the airline overbooked this flight? the probability is (Round to four decimal places as needed.)

Stress at work: In a poll about work, 50% of respondents said that their jobs were sometimes or always stressful. Eight workers are chosen at random. (a) What is the mean number who find their jobs stressful in a sample of 8 workers? Round the answer to two decimal places. The mean number who find their jobs stressful is (b) What is the standard deviation of the number who find their jobs stressful in a sample of 8 workers? Round the answer to four decimal places. The standard deviation of the number who find their jobs stressful is

Stress at work: In a poll about work, 82% of respondents said that their jobs were sometimes or always stressful. Ten workers are chosen at random. Round the answers to four decimal places (a) What is the probability that exactly 9 of them find their jobs stressful? The probability that exactly 9 of them find their jobs stressful is (b) What is the probability that more than 6 find their jobs stressful? The probability that more than 6 find their jobs stressful is (c) What is the probability that fewer than 5 find their jobs stressful? The probability that fewer than 5 find their jobs stressful is

A binomial experiment has the given number of trials and the given success probability p. n=16, p=0.2 (a) Determine the probability P(1 or fewer). Round the answer to at least four decimal places. P(1 or fewer) = (b) Find the mean. Round the answer to two decimal places. The mean is

High blood pressure: A national survey reported that 31% of adults in a certain country have hypertension (high blood pressure). A sample of 21 adults is studied. Round the answer to at least four decimal places. (a) What is the probability that exactly 5 of them have hypertension? The probability that exactly 5 of them have hypertension is (b) What is the probability that more than 7 have hypertension? The probability that more than 7 have hypertension is (c) What is the probability that fewer than 4 have hypertension? The probability that fewer than 4 have hypertension is

Your flight has been delayed: At Denver International Airport, 84% of recent flights have arrived on time. A sample of 12 flights is studied. Round the probabilities to four decimal places. (a) Find the probability that all 12 of the flights were on time. The probability that all 12 of the flights were on time is (b) Find the probability that exactly 10 of the flights were on time. The probability that exactly 10 of the flights were on time is (c) Find the probability that 10 or more of the flights were on time. The probability that 10 or more of the flights were on time is

Car inspection: Of all the registered automobiles in a city, 11% fail the emissions test. Fourteen automobiles are selected at random to undergo an emissions test. Round the answers to at least four decimal places. (a) Find the probability that exactly five of them fail the test. The probability that exactly five of them fail the test is (b) Find the probability that fewer than five of them fail the test. The probability that fewer than five of them fail the test is (c) Find the probability that more than four of them fail the test. The probability that more than four of them fail the test is

An airliner carries 400 passengers and has doors with a height of 74 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in. Complete parts (a) through (d). a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. The probability is. (Round to four decimal places as needed.)

If np ≥ 5 and nq 25, estimate P(at least 11) with n = 13 and p = 0.6 by using the normal distribution as an approximation to the binomial distribution; if np < 5 or nq<5, then state that the normal approximation is not suitable. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. P(at least 11)= (Round to three decimal places as needed.) B. The normal distribution cannot be used.

In a survey of 1084 people, 725 people said they voted in a recent presidential election. Voting records show that 64% of eligible voters actually did vote. Given that 64% of eligible voters actually did vote, (a) find the probability that among 1084 randomly selected voters, at least 725 actually did vote. (b) What do the results from part (a) suggest? (a) P(X≥ 725)= (Round to four decimal places as needed.) w

Use the chip model to find (-2) x 4. Show process. Your model needs to show (-2) x 4 rather than showing an equivalent expression such as - 2 x 4. Please use to represent -1 and use O to represent +1.

Question 10 (1 point) Sherlock and Mycroft each have a complete deck of cards. Each man picks one card at random from his deck. Each man has probabilities corresponding to his deck. The two cards chosen are "independent" of each other, which means that both-events- together have probabilities that multiply. If Sherlock and Mycroft each pick one card at random from their decks, what is the probability that both Sherlock gets a heart and Mycroft gets a heart?

John has a bucket with 300 glass marbles in it. 100 of the marbles have 'spots,' the rest of the marbles are one of the solid colors blue or green or black or white. If John draws one marble at random out of his bucket, what is the probability he DOES NOT gets a 'spots' marble?

What is the probability that your card is any 'black' card?

Draw one card at random from a well-shuffled deck. What is the probability that the card chosen is a 'spade, just not the ace of spades? Count outcomes carefully.

In a certain large city, 23% of cars are purple. If you pick a car in this city at random, what is the probability that you do NOT get a purple car?

What is the probability that a randomly drawn card is any ace?

What is the probability that the card drawn is the Ace of Hearts?

When you have equal probabilities, the probability of a Happy Event is ways-to-be-Happy/total-possibilities. John has a bucket with 300 glass marbles in it. 100 of the marbles have 'spots,' the rest of the marbles are one of the solid colors blue or green or black or white. If John draws one marble at random out of his bucket, each of the individual marbles is equally likely to be chosen. What is the probability he gets a 'spots' marble?

Sherlock has a well-shuffled complete deck of cards. John has a bucket with 300 glass marbles in it. 100 of the marbles have 'spots, the rest of the marbles are one of the solid colors blue or green or black or white. If Sherlock picks one card at random from his deck and John picks one marble at random from his bucket, the two events are independent of each other, and probabilities multiply. What is the probability that Sherlock gets a card and John gets a marble?

What is the probability that the card is any 'heart?'

The cholesterol levels of 14-year-old boys are Normally distributed with mean 17 mg/dL and standard deviation 30 mg/dL. Suppose you pick a 14-year-old boy at random and measure his cholesterol. What is the probability that his cholesterol is less than 140?

point) In a certain large city, 23% of cars are purple. This is a very large city. If we pick one car at random and set it aside, the rest of the cars are still 23% purple. Even if we pick two or three cars and set them aside, the rest of the cars are still 23% purple. If we choose three cars at random, the cars are 'independent' of each other. Probability for all three cars is therefore probability for each car, multiplied together. What is the probability that all three randomly chosen cars are purple?

If I roll one 4-sided die and one 10-sided die, what is the chance that the total number of spots is 10?

A pet store has 9 puppies, including 3 poodles, 4 terriers, and 2 retrievers. If Rebecka selects one puppy at random, the pet store replaces the puppy with a puppy of the same breed, then Aaron chooses a puppy at random. Find the probability that they both select a poodle. The probability is (Type an integer or decimal rounded to three decimal places as needed.)

A bag contains 36 red blocks, 48 green blocks, 22 yellow blocks, and 19 purple blocks. You pick one block from the bag at random. Find the theoretical probability. Write your answer as a fraction in simplest form in the form a/b. P(purple or not red)

Two fair number cubes are rolled. Determine whether the events are mutually exclusive. The sum is a prime number; the sum is less than 4. The sum is odd; the numbers are equal. Both numbers are odd; the sum is even. Both numbers are odd; the sum is even. The product is greater than 20; the product is a multiple of 3.

A standard number cube is tossed. Find the following probability. P(less than 3 or odd)

Which of the following are mutually exclusive events when a single card is chosen at random from a standard deck of 52 playing cards? Choose all that apply. a. Choosing a 6 and choosing a club. b. Choosing a 7 and choosing a jack. c. Choosing a 10 and choosing a heart. d. Choosing an ace and choosing an 8.

Mike and Ava decided to see who is better at the online game "Squashing Sweets. They each played three games. Mike's scores were 85, 122, and 117. Ava's scores were 107, 116, and 101. Who is the better player -Mike or Ava? Also, what information gives you confidence in your conclusion? Elimination Tool Select one answer A Ava is the better player since her scores are consistently above 100 points. B Mike is the better player since his median score is higher than Ava's highest score. C Mike is the better player. Although he had one bad game, two of his three scores were higher than two of Ava's three scores. D Mike and Ava are equally good at the game, since the average for both of their scores is the same. E There is not enough information to determine who is the better player, because the results from these three games may be simply due to chance.

A ball is drawn randomly from a jar that contains 7 red balls, 6 white balls, and 3 yellow balls. Find the probability of the given event. Write your answers as reduced fractions or whole numbers. (a) P(A red ball is drawn) = (b) P(The ball drawn is NOT red) = (c) P(A green ball is drawn) =

Assume that adults have IQ scores that are normally distributed with a mean of μ = 105 and a standard deviation o=20. Find the probability that a randomly selected adult has an IQ between 93 and 117. The probability that a randomly selected adult has an IQ between 93 and 117 is (Type an integer or decimal rounded to four decimal places as needed.)

You want to rent an unfurnished one-bedroom apartment in Durham, NC next year. The mean monthly rent for a random sample of 60 apartments advertised on Craig's List (a website that lists apartments for rent) is $1000. Assume a population standard deviation of $200. Construct a 95% confidence interval. CL = 0.95, a = 0.05

Hal and Renee play the following game. A bag has 14 tiles in it, each with a letter from the two word phrase the probability on it. Hal and Renee take turns drawing a tile, recording the letter, and placing the tile back in the bag. Renee earns a point if she draws a vowel. Hal earns a point if he draws a consonant. They decide that the letter y can be a vowel or a consonant. Is the following statement True or False. The game is fair because Hal and Renee have the same probability of drawing a winning letter. Select one: True False

USE THE INFORMATION BELOW TO ANSWER QUESTIONS 22 THRU 23 In recent years home lighting technology has changed dramatically due to the development of Light Emitting Diode (LED) bulbs. Although previously used mainly in traffic lights and although LED bulbs are more expensive than incandescent bulbs, they use approximately 90% less energy and they last up to 25 times longer than incandescent bulbs. It has been estimated that the average home saves $250 per year using LED bulbs rather than incandescent bulbs. One popular manufacturer of LED bulbs claim that nearly all of their 75-watt LEDs will last for more than 25,000 hours. Question 22 Suppose that a small company purchases 300 of these 75-watt LEDs with a guarantee that 97% of them will last for more than 25,000 hours. Assuming the guarantee is correct, what is the probability that at least 280 of them will last for more than 25,000 hours? 0.9669 0.9845 0.9741 1 pts 0.9997

In a survey of U.S. adults with a sample size of 2003, 358 said Franklin Roosevelt was the best president since World War II. Two U.S. adults are selected at random from this sample without replacement. Complete parts (a) through (d). (a) Find the probability that both adults say Franklin Roosevelt was the best president since World War II. The probability that both adults say Franklin Roosevelt was the best president since World War II is 0.032. (Round to three decimal places as needed.) (b) Find the probability that neither adult says Franklin Roosevelt was the best president since World War II. The probability that neither adult says Franklin Roosevelt was the best president since World War II is (Round to three decimal places as needed.)

A process yields 14% of defective items. If 100 items are randomly selected from the process, find the following probabilities (a) The probability that the number of defectives exceeds 15 (b) The probability that the number of defectives is less than 12

A coin is tossed 484 times. Use the normal curve approximation to find the probability of obtaining (a) between 226 and 254 heads inclusive; (b) exactly 245 heads; (c) fewer than 216 or more than 269 heads.

A pair of dice is rolled 120 times. What is the probability that a total of 7 occurs (a) at least 16 times? (b) between 24 and 30 times inclusive? (c) exactly 20 times?

A pair of dice is rolled 240 times. What is the probability that a total of 7 occurs (a) at least 28 times? (b) between 41 and 49 times inclusive? (c) exactly 40 times?