Probability Questions and Answers

The lifetime of batteries manufactured by a particular company is normally distributed with mean 100 hours and standard deviation 25 hours. In a pack of 50 batteries, how many are expected to have a lifetime of more than 110 hours? Give your answer correct to the nearest integer.

Suppose 4-year-olds in a certain country average 3 hours a day unsupervised and that most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.8 hours and the amount of time spent alone is normally distributed. We randomly survey one 4-year-old living in a rural area. We are interested in the amount of time the child spends alone per day.

A successful basketball player has a height of 6 feet 6 inches, or 198 cm. Based on statistics from a data set, his height converts to the z score of 3.38. How many standard deviations is his height above the mean? The player's height is standard deviation(s) above the mean. (Round to two decimal places as needed.) *****

Given A, B, and C are events with p(~A)=0.35, p(B)=0.45, p(~ANB)=0.1, p(-ANC)-0.15, p(BNC)=0.20, p(~ANBNC)=0.05, and p(~AuBUC)=0.8, find p(C).

How many cards must be drawn (without replacement) from a standard deck of 52 to guarantee that eight of the cards will be of the same suit.

Madison has a bag with 30 red marbles and 5 green marbles. She chooses one at random. What are the odds in favor of her selecting a red marble? (Type answer in form a:b)

A student plans to take 3 courses next term. If he selects them randomly from a list of 10 courses, 5 of which are science courses, what is the probability that all 3 will be science courses?

Given A and B are mutually exclusive events such that p(A)=0.3, p(B)=0.4. What is the value of p(A∩B)

John has six bills of paper money in the following denominations: $1, $5, $10, $20, $50, and $100 If he selects 3 bills at a time what is the probability of selecting a group that has an average value of at least $26? 0.60 0.50 0.45 0.55

A random sample of 1014 adults in a certain large country was asked "Do you pretty much think televisions are a necessity or a luxury you could do without?" Of the 1014 adults surveyed, 534 indicated that televisions are a lux without. Complete parts (a) through (e) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). p= 0.527 (Round to three decimal places as needed.) (b) Verify that the requirements for constructing a confidence interval about p are satisfied. ***** The sample can be assumed to be a simple random sample, the value of np (1-p) is 252.761, which is greater than or equal to 10, and the sample proportion. (Round to three decimal places as needed.) sample size and is stated to not be less than or equal (c) Construct and interpret a 95% confidence interval for the population proportion of adults in the country who believe that televisions are a luxury they could do without. Select the correct choice below and fill in any answer bc choice. (Type integers or decimals rounded to three decimal places as needed. Use ascending order.) OA. There is a % probability the proportion of adults in the country who believe that televisions are a luxury they could do without is between without is between. and believe that televisions are a luxury they could OB. We are % confident the proportion of adults in the country (d) Is it possible that a supermajority (more than 60%) of adults in the country believe that television is a luxury they could do without? Is it likely? It is that a supermajority of adults in the country believe that television is a luxury they could do without because the 95% confidence interval (Type an integer or a decimal. Do not round.) (e) Use the results of part (c) to construct a 95% confidence interval for the population proportion of adults in the country who believe that televisions are a necessity. Lower bound: Upper bound: (Round to three decimal places as needed.)

For a standard normal distribution, find: P(-1.58 <z<0.69) Round your answer to 4 decimal places (e.g. 0.0001). Hint: Use technology such as Normal Curve Calculator. Question Help: Video 1 Video 2 Video 3 Message instructor Calculator

If a seed is planted, it has a 70% chance of growing into a healthy plant. If 10 seeds are planted, what is the probability that exactly 2 don't grow? Round your answer to 4 decimal places (e.g. 0.0001). Hint: Use technology such as Binomial Calculator ¹.

For the experiment of rolling an ordinary pair of dice, find the probability that the sum will be odd or a multiple of 3. (You may want to use a table showing the sum for each of the 36 equally likely outcomes.) The probability that the sum of the pair of dice is odd or a multiple of 3 is. *****

P(E)=0.13, find the odds against E. What are the odds against E? Select the correct choice below and fill in the answer box(es) to complete your answer. A. The odds are 0.15 (Type an integer or a decimal.) OB. The odds are to (Type integers or decimals.) .....

Marina has learned that it typically rains 43% of the days in August in the city where she lives. Assuming that the probability of rain on each day is independent, find the expected number of days it would rain in Marina's city in two weeks during the month of August. Round your answer to the nearest whole number of days and give your answer as an integer only.

About 9% of the population has a particular genetic mutation. 500 people are randomly selected. Find the mean for the number of people with the genetic mutation in such groups of 500.

Assume that random guesses are made for seven multiple choice questions on an SAT test, so that there are n = 7 trials, each with probability of success (correct) given by p=0.45. Find the indicated probability for the number of correct answers.

Write a sample space for the following random experiment. A month of the year is chosen for a second honeymoon. Choose the correct sample space below. A. S=(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30) B. S={January, February, Monday, April, May, June, July, August, Saturday, October, November, December} C. S=(January, February, March, April, May, June, July, August, September, October, November, December} D. S= (Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday} E. S = {January, March, April, May, June, July, August, September, October, December}

Mariah buys a bag of cookies that contains 4 chocolate chip cookies, 6 peanut butter cookies, 9 sugar cookies and 4 oatmeal cookies. What is the probability that Mariah reaches in the bag and randomly selects an oatmeal cookie from the bag, eats it, then reaches back in the bag and randomly selects a chocolate chip cookie?

If P(E)= 0.13, find the odds against E. What are the odds against E? Select the correct choice below and fill in the answer box(es) to complete your answer. A. The odds are (Type an integer or a decimal.) B. The odds are to (Type integers or decimals.)

If the odds against event E are 7 to 13, what is the probability of E? The probability of event E is. (Simplify your answer.)

What are the odds against E? Select the correct choice below and fill in the answer box(es) to complete your answer. A. The odds are (Type an integer or a decimal.) B. The odds are to (Type integers or decimals.)

Compute the probability of event E if the odds in favor of E are 10 to 11. P(E)= (Type an integer or a fraction.)

If P(E)= 0.47, find the odds in favor of E. What are the odds in favor of E? Select the correct choice below and fill in the answer box(es) to complete your answer. A. The odds are (Type an integer or a decimal.) B. The odds are to (Type integers or decimals.)

Based on their previous record, a football club has a 65% chance of winning each match it plays. Assuming the probability of winning is independent from match to match, find the probability that the football club wins exactly 14 matches out of 25. Give your answer accurate to three significant figures.

Of 300 randomly selected medical students, 20 said that they planned to work in a rural community. Use this data to find a 95% confidence interval for the true proportion of all medical students who plan to work in a rural community. 0.0430 < p < 0.0904 0.0296 p<0.104 0.0384 p < 0.0949 0.0331 < p < 0.100

In a recent year, an author wrote 159 checks. Use the Poisson distribution to find the probability that, on a randomly selected day, he wrote at least one check. The probability is

A student plans to take 2 courses next term. If he selects them randomly from a list of 11 courses, 5 of which are science courses, what is the probability that all 2 courses selected will be science courses? The probability that all 2 courses selected will be science courses is

A certain virus infects one in every 200 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 10% of the time if the person does not have the virus. (This 10% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive". a) Find the probability that a person has the virus given that they have tested positive, i.e. find P(A|B). Round your answer to the nearest tenth of a percent and do not include a percent sign. P(A|B)= b) Find the probability that a person does not have the virus given that they test negative, i.e. find P(A' |B'). Round your answer to the nearest tenth of a percent and do not include a percent sign. P(A' |B')=

A lottery involves randomly selecting 4 digits from 0-9, inclusively, without replacement. What is the probability that all 4 digits selected are greater than 4. Use combinations to determine the probability The probability is (Type an integer or a simplified fraction.) .……..

A survey showed that 75% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 13 adults are randomly selected, find the probability that no more than 1 of them need correction for their eyesight. Is 1 a significantly low number of adults requiring eyesight correction? The probability that no more than 1 of the 13 adults require eyesight correction is (Round to three decimal places as needed.) ----

For 100 births, P(exactly 58 girls) = 0.0223 and P(58 or more girls) = 0.067. Is 58 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. The relevant probability is so 58 girls in 100 births a significantly high number of girls because the relevant probability is

A security guard from a building inspects the visitor's bag before they will be allowed to enter the buildings premises. From their previous records, 3% of people inspected have questionable items in their bags. What is the probability that a string of 15 people pass through successfully before an individual is caught with a questionable object?

You roll a six-sided die. Find the probability of each of the following scenarios. (a) Rolling a 5 or a number greater than 3 (b) Rolling a number less than 5 or an even number (c) Rolling a 4 or an odd number

A geneticist conducts an experiment with beans, one sample of offspring consisted of 444 green beans and 161 yellow beans. Based on these results, estimate the probability of getting an offspring bean that is green. Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol. prob = 3 Is the result reasonably close to the value of 4 yes % no that was expected?

Let X be a random variable with probability distribution function: f(x) = P(X= x) = where k is a constant. kx, k(6 - x)², 0, if if if x = 1, 2, 3 x = 4,5 x = any other integer Find the exact value of k. Give your answer as fraction in fully simplified form.

For a certain candy, 15% of the pieces are yellow, 15% are red, 20% are blue, 10% are green, and the rest are brown. a) If you pick a piece at random, what is the probability that it is brown? b) If you pick a piece at random, what is the probability that it is yellow or blue? c) If you pick a piece at random, what is the probability that it is not green? d) If you pick a piece at random, what is the probability that it is striped?

A bag contains 12 black, 18 yellow and 30 purple marbles. Joe pays $10 for the opportunity to pick a marble from the bag. If he picks a black marble, he gets $20. If he picks a yellow marble, he gets $15. If he picks a purple marble, he gets $k. The game is fair. Find the value of k. Give an exact answer.

For the experiment of rolling a single fair die, find the probability of obtaining not greater than 5. The probability of obtaining not greater than 5 is

The heights of adult males in the United States are approximately normally distributed. The mean height is 70 inches (5 feet, 10 inches) and the standard deviation is 3 inches. Estimate the probability that a randomly selected male is between 65.5 and 73 inches tall. 50% 23% 67% 77%

A plant manufactures part whose lengths are normally distributed with a mean of 16.3 centimeters and a standard deviation of 2.5 centimeters. Question: 20% of all parts are below what length? 16.00 20.01 14.20 10.00

A jar contains 6 pennies, 3 nickels and 4 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins. Round your answers to 3 decimal places. Find the probability X = 10. Find the probability X = 11.

Suppose that a box contains 7 cameras and that 5 of them are defective. A sample of 2 cameras is selected at random. Define the random variable X as the number of defective cameras in the sample. Write the probability distribution for X.Write your answer in fraction form or round to 3 decimal places.

Mr. Hayes is about to give one of his students a piece of candy for asking a good question in class. He's going to choose the piece of candy at random out of a bag he brings to class. The following pieces of candy are in the bag: 10 apple gumballs, 9 grape gumballs, 11 apple suckers, and 7 grape suckers. What is the probability that the piece of candy Mr. Hayes chooses is apple or is a gumball? Do not round intermediate computations, and round your answer to the nearest hundredth.

You roll a standard 6-sided die. Find the expected value for each experiment. (a) You earn 6 points for each dot on the side that lands up. (b) You earn 6 points if it lands on a prime number and lose 6 points if it does not land on a prime number.

Four jars of coins each contain 240 coins. The theoretical probability of randomly drawing a quarter is given in simplified form. Find the number of quarters in each jar.

In order to make a little money for the holidays, Marla is raising turkeys. The male of the species she selected has a mean weight of 17 lb at maturity and a standard deviation of 1.8 lb and their weights are normally distributed. What is the probability of raising a male turkey that weighs at least 21 lb at maturity? (21lbs and more)

a. If two people are selected at random, the probability that they do not have the same birthday (day and month) is 365/365+364/ 365 Explain why this is so. (Ignore leap years and assume 365 days in a year.) The first person can have any birthday, so they can have a birthday onof the 365 days. In order for the second person to not have the same birthday they must have one of the remaining birthdays. (Type whole numbers.)

An ice chest contains 6 cans of apple juice, 4 cans of grape juice, 7 cans of orange juice, and 4 cans of mango juice. Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting three cans of grape juice. The probability of selecting from the ice chest three cans of grape juice is. (Type an integer or a simplified fraction)

The probability that a certain state will be hit by a major tornado (category F4 or F5) in any single year is 17 Complete parts (a) through (d) below. ..... a. What is the probability that the state will be hit by a major tornado two years in a row? 0.00346 (Simplify your answer. Round to five decimal places as needed.) b. What is the probability that the state will be hit by a major tornado in three consecutive years? 0.00020 (Simplify your answer. Round to five decimal places as needed.) c. What is the probability that the state will not be hit by a major tornado in the next ten years? 0.545 (Round to three decimal places as needed.) d. What is the probability that the state will be hit by a major tornado at least once in the next ten years?