Exam 8: Probability

A bag contains 4 red marbles, 3 green ones, 3 white ones, and 1 purple one. Michelle reaches into the bag and grabs 5 of the marbles. Find the probability that she does not have all green ones.

Adoptions College instructors who adopt this book are (we hope!) three times as likely to continue to use the book the following semester as they are to drop it, whereas nonusers are eight times as likely to remain nonusers the following year as they are to adopt this book. Determine the probability that a nonuser will be a user in two years. In the long term, what proportion of college instructors will be users of this book

Write down the transition matrix associated with the state transition diagram.

The following table shows the results of a survey of 390 authors by a (fictitious) publishing company: New Authors Established Authors Total Successful 80 40 120 Unsuccessful 100 170 270 Total 180 210 390 ​ An unsuccessful author is chosen at random. Compute the estimated probability of the event that the unsuccessful author is established.

The following diagram shows the movement of U.S. households among three income groups - affluent, middle class, and poor - over the 12-year period 1965-1977. Assuming that the trend shown was to continue, what percent of households classified as affluent in 1965 were predicted to become poor in 1989 (Give your answer to the nearest .) According to the model, what percentage of all U.S. households will be in each income bracket in the long term (Give your answer to the nearest percent.) $a = 30.1$ , $b = 6.5$ , $c = 5.9$ , $d = 35.2$

A 2001 Agriculture Department study of more than 9,400 samples from more than 20 crops showed that 73% of conventionally grown foods had residues from at least one pesticide. Moreover, conventionally grown foods were six times as likely to contain multiple pesticide as organic foods. Of the organic foods tested, 23% had pesticide residues, which include 12% 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. ​

Determine whether the given information is consistent with a probability distribution. $P ( A ) = 0.1$ ; $P ( B ) = 0.4$ ; $P ( A \cap B ) = 0.1$

Suppose two dice (one green, one red) are rolled. Consider the following events. A: The red die shows 2. B: The numbers add to 4. C: At least one of the numbers is 2. D: The numbers do not add to 9. Express the following in symbols. "Either the numbers add to 4, or they add to 9, or the red die shows 2."

A bag contains 4 red marbles, 2 green ones, 2 white ones, and 1 purple one. Michelle reaches into the bag and grabs 5 of the marbles. Find the probability that she has at least 1 green marble.

In the New York State daily lottery game, a sequence of 6 (not necessarily different) digits in the range of 0-9 is selected at random. ​ Find the probability that all 6 are different. ​ If necessary, round your answer to four decimal places. ​ P = __________ ​

A pocket of gummy candy contains 5 strawberry gums, 5 lime gums, 3 black currant gums, and 3 orange gums. April May sticks her hand in and selects 6 at random. April is particularly fond of a combination of 3 strawberry and 3 black currant gums. Complete the following sentence: The event That April May will get the combination she desires is the set of... ​

According to a University of Maryland study of 200 samples of ground meats, the probability that one of the samples was contaminated by salmonella was 0.20. The probability that a salmonella-contaminated sample was contaminated by a strain resistant to at least one antibiotic was 0.86, and the probability that a salmonella-contaminated sample was contaminated by a strain resistant to at least three antibiotics was 0.54. Find the probability that a ground meat sample that was contaminated by an antibiotic-resistant strain was contaminated by a strain resistant to at least three antibiotics. Please round the answer to the nearest thousandth. ​

The following table shows hypothetical U.S. employment figures, broken down by educational attainment. All numbers are in millions and represent civilians aged 16 years and over. Those classed as "Not in Labor Force" were not employed nor actively seeking employment. Find the probability that a person was employed given that the person has less than 4 years of high school. Please round the answer to two decimal places. Employed Unemployed Not in Labor Force Total Less Than 4 Years High School 12.2 0.9 10.6 23.7 More than 4 Years High School 73.2 3 20.4 96.6 Total 85.4 3.9 31 120.3

Use the given transition matrix P and the given initial distribution vector v to obtain the two-step transition matrix and the distribution vector after two steps. $P = \left[ \begin{array} { c c } 0.9 & 0.1 \\0 & 1\end{array} \right]$ , $v = \left[ \begin{array} { l l } 0.9 & 0.1\end{array} \right]$

The following diagram shows the movement of U.S. households among three income groups - affluent, middle class, and poor - over the 11-year period 1982-1993. Assuming that the trend shown was to continue, what percent of households classified as affluent in 1982 were predicted to become poor in 2004 (Give your answer to the nearest .) According to the model, what percentage of all U.S. households will be in each income bracket in the long term (Give your answer to the nearest percent.) $a = 26.5$ , $b = 7.8$ , $c = 8.1$ , $d = 31.2$

Any athlete who fails the Enormous State University's women's soccer fitness test is automatically dropped from the team. Last year, Mona Header failed the test, but claimed that this was due to the early hour. (The fitness test is traditionally given at 5 AM on a Sunday morning.) In fact, a study by the ESU Physical Education Department suggested that 50% of athletes fit enough to play on the team would fail the soccer test, although no unfit athlete could possibly pass the test. It also estimated that 41% of the athletes who take the test are fit enough to play soccer. Assuming these estimates are correct, what is the probability that Mona was justifiably dropped Please, round your answer to four decimal places. The probability is __________.

Student admissions are based on the following table, which shows the profile, by Math SAT I scores, of admitted students at some university for the Fall 2004 semester. Determine the theoretical probability of the event: "An applicant had a Math SAT of 700 or above or was admitted." (Round your answer to the nearest 0.01). - - - - - Total Admitted 10 212 1,150 2,882 5,399 9,653 Not Admitted 743 3,506 9,079 12,230 5,150 30,708 Total Applicants 753 3,718 10,229 15,112 10,549 40,361

The table below shows the frequency of outcomes when two distinguishable coins are tossed 4,000 times and the uppermost faces were observed. What is the estimated probability that the second coin lands with heads up Outcome HH HT TH TT Frequency 1,200 900 850 1,050 Round your answer to four decimal places, if necessary.

Seven coins are tossed. What is the probability that there will be at most one head

A bag contains 4 red marbles, 3 green ones, 1 fluorescent pink one, 2 yellow ones, and 2 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."