Exam 8: Probability

Suzy grabs four marbles from a bag containing three white marbles and five blue marbles. Find the probability that exactly three of the marbles are blue. ​ Enter your answer as a fraction in lowest terms.

The following table shows the results of a survey of 410 authors by a (fictitious) publishing company: New Authors Established Authors Total Successful 90 10 100 Unsuccessful 120 190 310 Total 210 200 410 An author is chosen at random. Compute the estimated probability of the event that the author is unsuccessful.

In 2002, 39.8% of all light vehicles were cars, and the rest were pickups or SUVs. The probability that a severe side-impact crash would prove deadly to a driver depended on the type of vehicle he or she was driving at the time, as shown in the table. What is the probability that the victim of a deadly side-impact accident was driving a car Please, round your answer to two decimal places. Cars 1.0 Light Truck or SUV 0.3 The probability is __________.

​A bag contains 6 red marbles, 3 green ones, 3 yellow ones, and 1 black one. Michelle reaches into the bag and grabs 4 of the marbles. Find the probability that she has 2 yellow ones and 1 black and 1 green one. ​

Your company is considering offering 400 employees the opportunity to transfer to its new headquarters in Ottawa and, as personnel manager, you decide that it would be fairest if the transfer offers are decided by means of a lottery. Assuming that your company currently employs 50 managers, 50 factory workers, and 600 miscellaneous stuff, find the probability that all managers will be offered the opportunity and the probability that you will be offered the opportunity.

It rains in Spain an average of once in 10 days, and when it does, hurricanes have a 5% chance of happening in Hartford. When it does not rain in Spain, hurricanes have a 1% chance of happening in Hartford. What is the probability that it rains in Spain when hurricanes happen in Hartford Please, round your answer to four decimal places. ?

Two dice (one red and one green) are rolled, and the numbers that face up are observed. Test the pair of events for independence. ​ A: The red die is 2, 3, or 4; B: The green die is even. ​ A and B are __________ (dependent or independent).

A 2001 Agriculture Department study of more than 9,400 samples from more than 20 crops showed that 72% of conventionally grown foods had residues from at least one pesticide. Moreover, conventionally grown foods were six times as likely to contain multiple pesticides as organic foods. Of the organic foods tested, 23% had pesticide residues, which include 8% with multiple pesticide residues. Compute two probability distributions: one for conventional produce and one for organic produce, showing the estimated probabilities that a randomly selected product has no pesticide, has residues from a single pesticide, and has residues from multiple pesticides. ​ Round your answers to two decimal places, if necessary. ​ The probability distribution for conventional produce, showing the estimated probabilities that a randomly selected product has no pesticide is __________, has residues from a single pesticide is __________, has residues from multiple pesticides is __________. ​ The probability distribution for organic produce, showing the estimated probabilities that a randomly selected product has no pesticide is __________, has residues from a single pesticide is __________, has residues from multiple pesticides is __________.

The following table shows the results of a survey of 360 authors by a (fictitious) publishing company: New Authors Established Authors Total Successful 50 40 90 Unsuccessful 120 150 270 Total 170 190 360 A successful author is chosen at random. Compute the estimated probability of the event that the successful author is established.

In an experiment to test the effectiveness of the latest roach trap, the "Roach Resort"; 70 roaches were placed in the vicinity of the trap and left there for an hour. At the end of the hour, it was observed that 42 of them had "checked in" while the rest were still scurrying around. (Remember that "once a roach checks in, it never checks out.") If a roach begins outside the "Resort", what is the probability of it "checking in" by the end of 3 hours ?

In 2003, the probability that a randomly chosen bag of cement from the world supply was consumed in the one country was 0.04, while the probability that it was consumed in another country was 0.30. What is the probability that a randomly chosen bag of cement was consumed in neither country Enter your answer in decimal form, not as a fraction. The probability is __________.

Say whether the given pair of events is independent, mutually exclusive, or neither. ​ A: Your new skateboard design is a success. B: Your new skateboard design is a failure.

Two distinguishable dice are rolled. Complete the sentence. ​ There could be two mutually exclusive events that both contain outcomes in which the numbers facing up add to... ​

There is a 40% chance of rain today and a 52% chance of rain tomorrow. Assuming that the event that it rains today is independent of the event that it rains tomorrow, what is the probability that there will be no rain today or tomorrow Please round the answer to two decimal places. ?

The T $\Phi$$\Phi$ Sorority has a tough pledging program - it requires its pledges to master the Greek alphabet forward, backward, and "sideways". During the last pledge period, one - third(s) of the pledges failed to learn it backward and three quarters of them failed to learn it sideways; 7 of the 12 pledges failed to master it either backward or sideways. Because admission into the sisterhood requires both backward and sideways mastery, what fraction of the pledges were disqualified on this basis

A bag contains 4 red marbles, 2 green ones, 1 fluorescent pink one, 2 yellow ones, and 3 orange ones. Suzy grabs 4 at random. Find the probability of the event: "She gets one of each color other than fluorescent pink, given that she gets the fluorescent pink one."

This table shows the result of the Big Eight Conference for the 1990 college football season. This is referred to as a "perfect progression". Assuming the "Won" score for each team is chosen at random at range 0-7, Find the probability that the results is form a perfect progression. Team Won Lost Nebraska(NU) 7 0 Oklahoma(OU) 6 1 Oklahoma State(OSU) 5 2 Colorado(CU) 4 3 Iowa State(ISU) 3 4 Missouri(MU) 2 5 Kansas(KU) 1 6 Minnesota State(MSU) 0 7

This table shows the result of the Big Eight Conference for the 1990 college football season. This is referred to as a "perfect progression". Assuming the "Lost" score for each team is chosen at random at range 0-7, find the probability that the result is from a perfect progression. Team Won Lost Nebraska(NU) 7 0 Oklahoma(OU) 6 1 Oklahoma State(OSU) 5 2 Colorado(CU) 4 3 Iowa State(ISU) 3 4 Missouri(MU) 2 5 Kansas(KU) 1 6 Minnesota State(MSU) 0 7

The following table shows the results of a survey of 440 authors by a (fictitious) publishing company: New Authors Established Authors Total Successful 60 40 100 Unsuccessful 150 190 340 Total 210 230 440 An established author is chosen at random. Compute the estimated probability of the event that the established author is successful.

According to a study conducted by the Harvard School of Public Health, a child seated in the front seat who was not wearing a seatbelt was 84% more likely to be killed in an accident if the car had an air bag that deployed than if it did not. Airbags deployed in 25% of all accidents. For a child seated in the front seat not wearing a seatbelt, what is the probability that the airbag deployed in an accident in which the child was killed (Round your answer to two decimal places.) The probability is __________.