Probability Questions and Answers

During a recent year, there were 11.2 million automobile accidents, 5.7 million truck accidents, and 172,000 motorcycle accidents. Find the following probabilities. (a) If one accident is selected at random, find the probability that it is either a truck or motorcycle accident. P (truck or motorcycle accident)= (b) If one accident is selected at random, find the probability that it is not a truck accident. P (not truck accident)=

A single fair die is tossed. Find the odds in favor of rolling a number greater than 1. What are the odds in favor of rolling a number greater than 1? to (Simplify your answer.)

A gumball machine has 40 red, 30 white and 10 yellow gumballs in it, and you purchase one gumball at random. What are the odds against getting a yellow gumball?

Find the indicated probability. If you pick a card at random from a well shuffled deck, what is the probability that you get a face card or a spade? 1/13 1/2 15/26 11/26

According to a disease control center, 40% of people in a certain country have high blood pressure. If a person in this country is selected at random, determine the odds in favor of this person having high blood pressure. 5:3 5:2 2:5 2:3 3:2 3:5

Of the last 75 people who went to the cash register at a department store, 19 had blond hair, 21 had black hair, 30 had brown hair, and 5 had red hair. Determine the empirical probability that the next person to come to the cash register has red hair. 2/5 14/15 21/25 1/15 3/5 19/25

From the sample space S={1, 2, 3, 4,..., 15) a single number is to be selected at random. Given event A, that the selected number is even, and event C, that the selected number is a prime number, find P(CIA). P(CIA)= (Simplify your answer. Type an integer or a fraction.)

From the sample space S= {1, 2, 3, 4,..., 15) a single number is to be selected at random. Given event A, that the selected number is even, and event B, that the selected number is a multiple of 4, find P(A/B). P(A/B)= (Simplify your answer. Type an integer or a fraction.)

A pet store has 9 puppies, including 2 poodles, 2 terriers, and 5 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. The probability is (Type an integer or a fraction.)

You are dealt one card from a standard 52-card deck. Find the probability of being dealt a card greater than 5 and less than 10. The probability of being dealt a card greater than 5 and less than 10 is (Type an integer or a simplified fraction.)

Assume that cans of Coke are filled so that, the actual amounts have a mean of 12 oz and standard deviation of 0.14 oz. If a random sample of 40 cans of Coke is selected, hind the probability that the mean content is: a) At least 12.16 oz ? b) Less than 11.94 OZ

If three people are selected, find the probability that all three were born in January. Write your answer as a fraction in simplest terms. The probability that all three people were born in January is

A produce buyer for a juice company is buying pears. He makes a choice of either Oregon, California, or imported pears. For this contract he must also choose fancy or extra fancy. Write out the sample space and assume each outcome is equally likely. Then give the probability of the requested outcomes in parts (a) and (b) below. Write out the sample space. Choose the correct answer below. A. S={(California,fancy), (California,extra fancy), (Oregon,fancy), (Oregon,extra fancy), (Michigan, fancy), (Michigan,extra fancy), (imported, fancy), (imported,extra fancy)} B. S={(California,fancy), (California,extra fancy), (Oregon,fancy), (Oregon,extra fancy), (imported, fancy), (imported extra fancy)} C. S={(California,fancy), (Oregon,fancy), (Oregon,extra fancy), (imported extra fancy)} D. S={(California,fancy), (Oregon,extra fancy), (imported,extra fancy)} (a) The pears selected are fancy. (Type an integer or a simplified fraction.) (b) The pears selected are imported or fancy. (Type an integer or a simplified fraction.)

A physical therapist is scheduling appointments for the day. She has five worker's comp cases and six Medicare patients awaiting care. If she chooses nine at random for her morning schedule, find the probability that she'll pick three worker's comp cases and six Medicare patients. Round your answer to five decimal places.

A beverage company announced in the last year that 60% of their products had discounts, 70% of their products were sugar-free and 40% were both. What is the portion of products that either had discounts or were sugar-free? Assume Event A: the product had discounts; Event B: the product was sugar-free.

Use the Venn diagram to answer the question. In 2016, among the top 100 grossing movies in a particular country, 17 were rated PG-13 and earned over $100 million. The number of movies that were rated PG-13 that earned less than $100 million was 21. The number of movies that were not rated PG-13 that earned less than $100 million was 31. What was the number of movies that earned over $100 million and that were not rated PG-13? FERRE The number of movies that earned over $100 million and were not rated PG-13 was (Type a whole number.)

In a group of seven Olympic track stars, three are hurdlers. If three track stars are selected at random without replacement, find the probability that they are all hurdlers. Express your answer as a decimal rounded to four places if necessary. P (All three are hurdlers) =

A marble is drawn from a box containing 2 yellow, 3 white, and 19 blue marbles. Find the odds in favor of drawing the following. (a) A yellow marble (b) A blue marble (c) A white marble

Given events A and B are mutually exclusive events, that is, A and B are mutually exclusive events with P(A)=0.2, P(B)=0.3, find P(A∩B).

When playing American roulette, the croupier (attendant) spins a marble that lands in one of the 38 slots in a revolving turntable. The slots are numbered 1 to 36, with two additional slots labeled 0 and 00 that are painted green. Assume a single spin of the roulette wheel is made. Find the probability of winning with the given bet. An example of a dozen bet is betting that the marble will land in a slot numbered 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, or 23. and the number of outcomes in the event is The total number of outcomes is (Type integers or simplified fractions.) The probability of winning with the given dozen bet is (Simplify your answer.)

Given events A and B are events with P(-(A u B))=2/3, we can determine the probability of which other event in the list below has the same probability? ANB AUB -AN-B -Au-B -(ANB) -(-AN-B) -(-Au-B)

In a conference, 75% of the attendees have been to Germany, and 15% of the attendees have been to both England and Germany. What is the probability that a randomly selected attendee has been to England, if it is known that they have been to Germany? Assume Event E: the attendee has been to England; Event G: the attendee has been to Germany.

In a class of 26 students, 17 have a brother and 12 have a sister. There are 5 students who do not have any siblings. What is the probability that a student has a brother given that they have a sister?

The faces of a fair cube are numbered 1 through 6; the probability of rolling any number from 1 through 6 is equally likely. If the cube is rolled twice, what is the probability that an even number will appear on the top face in the first roll or that the number 1 will appear on the top face in the second roll?.

A species of snakes studied in a certain area in South America has some exceptionally large individuals, for some reason yet unknown to scientists. The weights of the studied population are strongly right-skewed with mean 36 kg and standard deviation 7 kg. A random sample of 75 snakes is taken. What is the probability that the mean weight of the sample is greater than 37 kg? 0 0.1075 0.4432 cannot say

Four coins are tossed several times. Which of the following represents the outcome on a coin that may not be fair? 1st coin is tossed 50 times and gives 24 heads and 26 tails. 2nd coin is tossed 250 times so that P(heads) = 0.25. 3rd coin is tossed 16 times and gives P(tails) = 9/16 4th coin is tossed 25,000 times and gives 12,505 heads.

The mean wage at a company is $25 an hour with a standard deviation of $3 an hour. What is the probability that a worker earns between $22 and $34 an hour? Use the 68-95-99.7 normal distribution curve.

Let S be the event that a randomly chosen voter supports the president. Let W be the event that a randomly chosen voter is a woman. Identify the answer which expresses the following with correct notation: The probability that a randomly chosen voter is a woman, given that the voter supports the president. Select the correct answer below: P(WIS) P(S AND W) P(W) AND P(S) P(SW)

among automobiles of a certain make, 23% require service during a one-year warranty period. A dealer sells 87 of these vehicles. a.) Approximate the probability that 25 or fewer of these vehicles require repairs. b.) Approximate the probability that more than 17 vehicles require repairs.

The duration of a professor's class has a continuous uniform distribution between 50.0 minutes and 52.0 minutes. If one class is randomly selected, find the probability that the professor's class duration is between 51.2 and 51.5 minutes. P(51.2 < X < 51.5) =

If two six-sided dice are rolled, then the sum of the dice is an example of a continuous random variable. true false

A ball is drawn randomly from a jar that contains 3 red balls, 7 white balls, and 4 yellow balls. Find the probability of the given event, and please show your answers as reduced fractions. (a) A red ball is drawn. P(red). (b) A white ball is drawn. P(white) (c) A yellow ball or red ball is drawn. P(yellow or red)

A poll showed that 59.9% of Americans say they believe that life exists elsewhere in the galaxy. What is the probability of randomly selecting someone who does not believe that life exists elsewhere in the galaxy. Probability=

A special deck of cards has 5 blue cards, and 3 yellow cards. The blue cards are numbered 1, 2, 3, 4 and 5. The yellow cards are numbered 1, 2, and 3. The cards are well shuffled and you randomly draw one card. A card drawn is yellow B = card drawn is even-numbered a) How many elements are there in the sample space? b) P(A) = Please enter a reduced fraction c) P(B) = Please enter a reduced fraction

A group of people were asked if Marilyn Monroe had an affair with JFK. 467 responded "yes", and 487 responded "no". Find the probability that if a person is chosen at random, he does NOT believes Marilyn Monroe had an affair with JFK. Probability (Please enter a reduced fraction.)

Ajar contains 12 red marbles numbered 1 to 12 and 6 blue marbles numbered 1 to 6. A marble is drawn at random from the jar. Find the probability of the given event, please show your answers as reduced fractions. (a) The marble is red. P(red) = (b) The marble is odd-numbered. P(odd) = (c) The marble is red or odd-numbered. P(red or odd) = (d) The marble is blue or even-numbered. P(blue or even) =

According to a goverment statistics department, 19.8% of women in a country aged 25 years or older have a Bachelor's Degree, 15.8% of women in the country aged 25 years or older have never married; among women in the country aged 25 years or older who have never married, 23.8% have a Bachelor's Degree; and among women in the country aged 25 years or older who have a Bachelor's Degree, 19.0% have never married. Complete parts (a) and (b) below.

A die is rolled 3 times. What is the probability of showing a (n) 2 on every roll?

There are 10 balls in a bag: 5 red, 2 blue, 2 green, and 1 yellow. Answer each question by reporting probability as a simplified fraction, a decimal, or a percent. Part A: If you draw one ball from the bag, what is the probability of drawing a red ball? Part B: If you flip a coin and draw a ball from the bag, what is the probability of "tails" and "green"? Part C: If you draw a yellow ball first and do not replace it, what is the probability of drawing blue on the second ball? Part D: What is the probability that you will draw yellow first and blue second?

Antibiotic resistance occurs when disease-causing microbes no longer respond to antibiotic drug therapy. Because such resistance is typically genetic and transferred to the next generations of microbes, it is a very serious public health problem. Gonorrhea is the second most commonly reported notifiable disease in the United States. According to the Centers for Disease Control and Prevention (CDC), 27% of gonorrhea cases tested in 2010 were resistant to at least one of the three major antibiotics commonly used to treat this sexually transmitted disease. The CDC reported that 38% of gonorrhea cases tested in 2014 were resistant to at least one of the three major antibiotics commonly used to treat gonorrhea. (a) In 2010, out of 10 randomly selected gonorrhea cases, what is the mean of the count of cases X showing resistance to at least one of the three major antibiotics? (Enter your answer rounded to one decimal place.)

In a test for ESP (extrasensory perception), a subject is told that cards only the experimenter can see contain either a star, a circle, a wave, or a square. As the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. A subject who is just guessing has probability 0.25 of guessing correctly on each card. (a) The count of correct guesses in 20 cards has a binomial distribution. What is the value of n? (Enter your answer as a whole number.) n= What is the value of p? (Enter your answer rounded to two decimal places.) P=

Blood type AB is somewhat rare in the United States (it is found in 4% of the general population). It is particularly useful for plasma transfusions because this plasma can be accepted by individuals with all blood types. The plasma is the liquid part of the blood once all cells are removed. You count the number X of AB donors who come to a fixed Red Cross location per day. This count has the Poisson distribution, with parameter being the mean number of AB donors per day. (a) The donation center sees an average of 2.1 AB donors per day. Find the Poisson probabilities for X = 0, 1,2,3,4,5. P(X = 0) = P(X= 1) = P(X=2)=

A modified roulette wheel has 28 slots. One slot is 0, another is 00, and the others are numbered 1 through 26, 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? The probability of winning is (Type an integer or a simplified fraction.)

A group of researchers found that the probability of completing a given task was 0.61. They then took a random sample of n = 66 people. (a) What is the value of n*p? Use 2 decimal places in answering this and the next question. (b) What is the value of n*(1 - p)? (c) Determine whether the following statement is true or false. We can conclude that the sampling distribution of the sample proportion is approximately normal. True, because both n*p and n*(1 p) are both greater than or equal to 15 and the CLT applies. True, because only n*P has to be greater than or equal to 15 for the CLT to apply. False, because both n*p and n*(1 - p) are both greater than or equal to 15 and the CLT applies. False, because both n*p and n*(1 - p) are less than 15 and the CLT does not apply.

Consider a population of size N = 12, 100 with a mean of u 200 and standard deviation of o = 15. Compute the following 2-values for sampling distributions of with given sample size. Suppose a random sample of 56 observations is selected from the population. Calculate the z-value that corresponds to x̄ = 206. Suppose a random sample of 77 observations is selected from the population. Calculate the z-value that corresponds to x̄ 198. Suppose a random sample of 60 observations is selected from the population. Calculate the z-value that corresponds to x̄ = 205 Suppose a random sample of 69 observations is selected from the population. Calculate the 2-value that corresponds to x̄ = 200.

10) A newspaper advertises 5 different movies, 3 plays, and 2 baseball games for the weekend. If a couple selects 3 activities, find the probability that they attend a. 2 plays and 1 movie. b. Three movies c. Two plays and 1 baseball d. 1 of each type.

The distribution of all Indian River County grapefruit weights is known to be normally distributed with a mean of 296 grams and a standard deviation of 35 grams. Use this information to determine the following probabilities. Round solutions to four decimal places, if necessary. Find the probability that a random sample of 52 grapefruit has a mean weight greater than 292 grams. P(x > 292) = Find the probability that a random sample of 52 grapefruit has a mean weight between 292 and 295 grams. P(292< x < 295) =

Sometimes it is easier to figure out the probability that something will not happen than the probability that it will. When finding the probability that something will m happen, you are looking at the complement of an event. The complement is the set of all outcomes in the sample space that are not included in the event. Show two ways to solve the problem below, then decide which way you prefer and explain why. a. The marketing department has interviewed people of all different age groups about the BBQ chicken salad, but now they need information about why the othe salads are less popular. What is the probability that the next person randomly chosen will not prefer the BBQ chicken salad? b. If the probability of an event A is represented symbolically as P(A), how can you symbolically represent the probability of the complement of event

On a certain day, a cheese packaging facility packaged 480 units of mozzarella cheese. Some of these packages had major flaws, some had minor flaws, and some had both major and minor flaws The following table presents the results. minor flaw no minor flaw major flaws no major flaws 19 33 66 362 Find the probability that a randomly selected package of mozzarella cheese from this facility has a minor flaw. 0.177 0.137 0.108 0.235

If a procedure meets all the conditions of a binomial distribution except that the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by P(x) = p(1-p)x-1 where p is the probability of success on any one trial. Assume that the probability of a defective computer component is 0.17. Find the probability that the first defect is found in the fifth component tested.