Probability Questions and Answers

Assume that a procedure yields a binomial distribution with n = 83 trials and the probability of success for one trial is p = 0.86. Find the mean for this binomial distribution. (Round answer to one decimal place.) μ= Find the standard deviation for this distribution. (Round answer to two decimal places.) σ=

Find the z-score corresponding to the given value and use the z-score to determine whether the value is unusual. Consider a score to be unusual if its z-score is less than -2.00 or greater than 2.00. Round the z-score to the nearest tenth if necessary. A body temperature of 96.7° F given that human body temperatures have a mean of 98.20° F and a standard deviation of 0.62⁰.

For the following problems, calculate the probability of each event for one roll of a die. Hint: Use the formula for theoretical probability. 12) a number greater than 6

A machine that manufactures automobile parts produces defective parts 12% of the time. If 9 parts produced by this machine are randomly selected, what is the probability that fewer than 2 of the parts are defective? Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places. (If necessary, consult a list of formulas.)

A college reported the following based on their graduation data. 60% of freshman had attended public schools. 60% of freshman who had attended public schools graduated within 5 years. 80% of other freshman graduated within 5 years. What percent of freshman graduated within 5 years? A. 68% B. 66% C. 47% D. 69%

If the probability of winning a race is 1/3 What are the odds in favor of winning the race?

A machine has 11 identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the machine will be working. 0.949 0.839 0.162 0.111

The probability that an event will not happen is P (E') The probability that the event will happen is (Type an integer or a simplified fraction.) Find the probability that the event will happen.

Let's say you devise a blackjack strategy where you win 42% of the time, tie 9% of the time, and lose 49% of the time. When you lose you lose $1, on a tie you gain $0, and on a win you gain $1 (assume you aren't allowed to split or double). What is the expected value of your winnings? Note: Do not round your answer.

A student in the sophomore class has an equal chance of being in room 1, 2, 3, 4, or 5 for any of her six classes. What is the probability that she will be in room 3 for at least one class? 0.80 0.74 0.26 0.14

You write the numbers 1-10 on slips of paper and throw them into a hat. If you pull out a 7 first and do not replace it, the probability of pulling out an 8 is 1/10 1/8 1/9 1/5

Which number represents the probability of an event that is very likely to occur? A 0.12 B 1.3 C 0.89 D 0.09

For Pam, the probability of getting diabetes (event A) is 0.35, and the probability of having thyroid problems (event B) is 0.28. The probability of getting both is 0.098. Are events A and B dependent or independent? Show your work.

If the following is a probability distribution, what is the probability of 3? x 0 1 2 3 P(x) 1/8 1/8 3/8 ? a. 5/8 b. 1/8 c. 1 d. 3/8

In 1970, 11% of people in a certain region completed four years of college, 40% of them were women. In 1990, 19% of people in the same region completed four years of college: 53% of them were women Complete parts (a) through (c) below. In each part below, a person is selected at random from the region (a) Given that a person completed four years of college in 1970, what is the probability that the person was a woman? The probability is (b) What is the probability that a woman finished four years of college in 1990? The probability is (c) What is the probability that a person was not a male college graduate in 1990? The probability is

Suppose z is the standard normal variable. Draw the normal curve for each of the following probability statements to visualize the required area. Report answers accurate to at least 4 decimal places. a. P(Z < -0.03)= b. P(z > -1.19) = c. P(Z < 0) = d. P(Z < 4.33) = e. P(-1.55 < z < 0.31) = f. P(-1.63 < z < 0) = g. P(z<-0.9 given z < 0) = h. P(z < -1.51 or z > 0.31) =

In Australia in 1995, of the 2907 indigenous people in prison 17 of them died. In that same year, of the 14501 non-indigenous people in prison 42 of them died ("Aboriginal deaths in," 2013). a. Find the probability that an indigenous person in prison dies. Enter your answer as a fraction. Enter your answer rounded to 3 decimal places b. Find the probability that a non-indigenous person in prison dies. Enter your answer as a fraction. Enter your answer rounded to 3 decimal places

When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 55 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3 batteries do not meet specifications. A shipment contains 6000 batteries, and 2% of them do not meet specifications What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected? The probability that this whole shipment will be accepted is (Round to four decimal places as needed.)

The lengths of pregnancies are normally distributed with a mean of 267 days and a standard deviation of 15 days. a. In a letter to an advice column, a wife claimed to have given birth 308 days after a brief visit from her husband, who was working in another country. Find the probability of a pregnancy lasting 308 days or longer. What does the result suggest? b. If the length of pregnancy is in the lowest 3%, then the baby is premature. Find the length that separates premature babies from those who are not considered premature. a. The probability that a pregnancy will last 308 days or longer is (Round to four decimal places as needed.)

If a candy jar has 21 green jelly beans and 12 black jelly beans, and 19 red jelly beans, what is the probability of eating a green and then a red jelly bean? Express the probability to the nearest hundredth.

Based on historical data, your manager believes that 31% of the company's orders come from first-time customers. A random sample of 100 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.27

In a certain weather forecast, the chances of a thunderstorm are stated as "1 in 25." Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. The probability is____

Let C be the event that a randomly chosen person has a pet cat. Let D be the event that a randomly chosen person has a pet dog. Identify the answer which expresses the following with correct notation: Of all the people who have a pet cat, the probability that a randomly chosen person has a pet dog. Select the correct answer below: O P(DIC) O P(C AND D) O P(D) AND P(C) O P(CID)

Let G be the event that a randomly chosen student is a girl. Let S be the event that a randomly chosen student plays sports. Identify the answer which expresses the following with correct notation: Given that the student is a girl, the probability that a randomly chosen student plays sports. Select the correct answer below: P(SIG) P(G|S) P(G AND S) P(S) AND P(G)

In a local survey, 100 citizens indicated their opinions on a revision to a local land-use plan. Of the 62 persons giving favorable responses, 40 were males. Of the 38 giving unfavorable responses, 15 were males. If one citizen is randomly selected, find the probability that person is male and has a favorable opinion. 0.40 0.65 0.62 0.55 0.25

A bin contains seven red chips, nine green chips, three yellow chips, and six blue chips. Find the probability of drawing a yellow chip, not replacing it, and then choosing a blue chip. 3/100 9/625 3/200 18/625

Assume that Jim, Bruce, Valerie, and Simon are four of the 15 members of the class, and that four of the class members will be chosen randomly to deliver their reports during the next class meeting. What is the probability that Jim, Bruce, Valerie, and Simon are selected in that order? The probability that Jim, Bruce, Valerie, and Simon are selected in that order is (Type an integer or decimal rounded to six decimal places as needed.)

A certain medical test is known to detect 79% of the people who are afflicted with the disease Y. Type numbers in the boxes. If 10 people with the disease are administered the test, what is the probability that the test will show that: All 10 have the disease, rounded to four decimal places? At least 8 have the disease, rounded to four decimal places? At most 4 have the disease, rounded to four decimal places?

Construct the sample space for a probability experiment where a coin is flipped, and then a 10-sided die is rolled. (H1, H2, H3, H4, H5, H6, H7, H8, H9, H10, T1, T2, T3, T4, T5, T6, T7, T8, T9, T10) This setup was used for a carnival game, and different amounts paid out for certain outcomes. Find the probability of each outcome: (a) There was a head on the coin and an odd number on the die. (b) There was a head on the coin and a prime number on the die. (c) There was a head on the coin and a number less than on the die. Write your answers in exact, simplified form.

- In a class with 50 students, 25 of the students are sophomores, 15 of the students are mathematics majors, and 10 of the mathematics majors are sophomores. If a student in the class is to be selected at random, what is the probability that the student selected will be a sophomore or a mathematics major or both? A) 0.4 (B) 0.5 (C) 0.6 (D) 0.8

IMPROVING QUALITY - THE WRITE RIGHT COMPANY MANUFACTURERS BALLPOINT PENS AND HAS BEEN EXPERIENCING A 6% RATE OF DEFECTIVE PENS. MODIFICATIONS ARE MADE TO THE MANUFACTURING PROCESS IN AN ATTEMPT TO IMPROVE QUALITY. THE MANAGER CLAIMS THAT THE MODIFIED PROCEDURE IS BETTER BECAUSE A TEST OF 60 PENS SHOWS THAT ONLY ONE IS DEFECTIVE. A) ASSUMING THAT THE 6% RATE OF DEFECTS HAS NOT CHANGED, FIND THE PROBABILITY THAT AMONG 60 PENS, EXACTLY ONE IS DEFECTIVE.

Makayla has a bag that contains orange chews, cherry chews, and watermelon chews. She performs an experiment. Makayla randomly removes a chew from the bag, records the result, and returns the chew to the bag. Makayla performs the experiment 50 times. The results are shown below: A orange chew was selected 14 times. A cherry chew was selected 12 times. A watermelon chew was selected 24 times. Based on these results, express the probability that the next chew Makayla removes from the bag will be orange or cherry as a fraction in simplest form.

Use the following statement to answer parts a) and b). Two hundred raffle tickets are sold for $3 each. One prize of $400 is to be awarded. Winners do not have their ticket costs of $3 refunded to them. Raul purchases one ticket. a) Determine his expected value. b) Determine the fair price of a ticket. a) His expected value is $. (Type an integer or a decimal.) b) The fair price of a ticket is $. (Type an integer or a decimal.)

A TV studio has brought in 7 boy kittens and 9 girl kittens for a cat food commercial. The director is going to choose 6 of these kittens at random to be in the commercial. What is the probability that the director chooses 4 boy kittens and 2 girl kittens? Round your answer to three decimal places.

Find a 95% confidence interval for the mean of the length of fishes in a pond based on the sample below. The measurements are in inches. 5, 6, 6, 7, 9, 9, 10, 11, 11, 12, 12, 12, 13, 14, 19 (8.62, 12.18) (8.63, 12.17) (8.69, 12.11) 8.56, 12.20)

In an article on Flurry Blog, a gaming marketing gap for men between the ages of 30 and 40 is identified. You are researching a startup game targeted at the 35- year-old demographic. Your idea is to develop a strategy game that can be played by men from their late 20s through their late 30s. Based on the article's data, industry research shows that the average strategy player is 28 years old with a standard deviation of 4.8 years. You take a sample of 100 randomly selected gamers. If your target market is 29- to 35-year-olds, should you continue with your development strategy?

Al Gorithm is going on vacation. He is in his room trying to decide what outfits he wants to bring. He has a total of 50 shirts and 10 shorts. Once he picks a clothing item, he puts it in his luggage. If asked to calculate a probability of picking his next clothing item, would it be considered a dependent or independent event?

The numbers 1 through 8 are written in separate slips of paper, and the slips are placed into a box. Then, 4 of these slips are drawn at random. What is the probability that the drawn slips are "1", "2", "3", and "4", in that order? (A) 0.01429 (B) 0.34296 (C) 0.000595 (D) 0.01428

Find each probability. Express the result as a decimal rounded to the nearest thousandth and then as a reduced fraction. a). Given P(A) = 0.4 and P(B) = 0.2. If A and B are independent events, what is P(A and B)? b). Given P(A) = 0.3 and P(B|A) = 0.6. If A and B are dependent, what is P(A and B)

A fair die is rolled 6 times. What is the probability of having no 1 and no 2 among the rolls? Round your answer to three decimal places.

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

The table below cross classifies the price of 486 stocks in a particular stock exchange, with whether the earnings per share ratio was positive or not. Use the data in the table find the probability that the price of the stock is $50.00-$99.99 or the earnings per share ratio is positive. Earnings per Share Price of Stock Negative or 0 Positive $0-$49.99 25 123 $50.00-$99.99 18 180 $100.00 or higher 2 138 A). P(E)=180/100 b)P(E) =18/(123+180 +138) C). P(E)= 180/486 D). P(E)=(123+18+180 +138)/486 The probability that the price of the stock is $50.00-$99.99 or the earnings per share ratio is positive is

A citizen's delegation to Queen's Park is to be formed by selecting ten names at random from a box. The box contains the names of 20 citizens from Bolton, and 12 citizens from Brampton. What is the probability that the delegation will consist of five citizens from each city? a. 0.1903 b. 0.00312 c. 0.00200 d. 0.01982

Whenever Nicole rents a movie from iTunes, the probability that it will be a comedy is 52%. Of the next seven movies she rents, what is the probability that she rents no more than two comedies?

A bean bag is randomly thrown onto the square table top shown and does not touch a line. Determine the probability that the bean bag lands on a green area. P(green)=__________

Each individual letter of the word Oklahoma is placed on a piece of paper, and all 8 pieces of paper are placed in a hat. If one letter is selected at random from the hat, find the probability that a vowel is selected. P (vowel) = ___________

Betty has several of the standard six-sided dice that are common in many board games. If Betty rolls one of these dice, what is the probability that: She rolls a three. ▢ She rolls a five. ▢ She rolls a three or a five. ▢ She rolls an even number. ▢

Fill in the blank. If n(E1 and E2) = 4 and n(E1) = 16, then P(E2 | E1) = _______. If n(E1 and E2) = 4 and n(E1)= 16, then P(E2 | E1) = _______ (Type an integer or a simplified fraction)

The table shows the results of a survey of patrons of a particular restaurant chain. Meals Good Service Poor Service Total Lunch 527 315 842 Dinner 923 612 1535 Total 1450 927 2377 If one of these patrons is selected at random, find the probability that their service was good, given that their meal was dinner. The probability that their service was good, given that their meal was dinner, is ______. (Round to four decimal places as needed.)

A computer salesperson at Best Buy claims that she has a 18% chance of selling a computer when helping out a customer. If this is true and she talks to four customers before lunch, find the probability that all four will buy computers. Round your answer to at least four decimal places.