Exam 8: Probability

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.

In 2000, 86% of all Caucasians in the U.S., 77% of all African-Americans, 77% of all Hispanics, and 85% of residents not classified into one of these groups used the Internet for e-mail. At that time, the U.S. population was 69% Caucasian, 12% African-American, and 13% Hispanic. What percentage of U.S. residents who used the Internet for e-mail were Hispanic Express your answer to the nearest 1%. The answer is __________%

The following table shows the results of a survey of 380 authors by a (fictitious) publishing company: New Authors Established Authors Total Successful 80 20 100 Unsuccessful 120 160 280 Total 200 180 380 ​ An established author is chosen at random. Compute the estimated probability of the event that the established author is successful.

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 in the range 500 - 599 or was admitted." (Round your answer to the nearest 0.01). - - - - - Total Admitted 5 212 1,120 2,882 5,346 9,565 Not Admitted 628 3,507 9,289 12,230 5,150 30,804 Total Applicants 633 3,719 10,409 15,112 10,496 40,369 ​ Enter your answer in decimal form, not as a fraction. The probability is __________.

The phrase "Dogs of the Dow" refers to the stocks listed in the Dow with the highest dividend yield. This table shows the top ten stocks of the "Dogs of the Dow" list. If you selected four of these stocks at random, what is the probability that your selection included the company with the highest yield and excluded the company with the lowest yield Symbol Company Yield SBC SBC Communications 5.46\% GM General Motors 5.46\% MRK Merck 5.42\% MO Altria 4.62\% VZ Verizon 4.32\% JPM JP Morgan Chase 3.78\% C Citigroup 3.64\% PFE Pfizer 3.12\% DD DuPont 2.96\% GE General Electric 2.46\%

The following table shows the results of a survey of 370 authors by a (fictitious) publishing company: New Authors Established Authors Total Successful 60 20 80 Unsuccessful 140 150 290 Total 200 170 370 A new author is chosen at random. Compute the estimated probability of the event that the new author is unsuccessful.

Write down the transition matrix associated with the given state transition diagram below. ​ ​ $A = \frac { 3 } { 5 }$ , $B = \frac { 2 } { 5 }$ , $C = \frac { 2 } { 3 }$ , $D = \frac { 1 } { 3 }$

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 was admitted." (Round your answer to the nearest 0.01). - - - - - Total Admitted 6 212 1,124 2,882 5,297 9,521 Not Admitted 687 3,501 9,547 12,230 5,150 31,115 Total Applicants 693 3,713 10,671 15,112 10,447 40,636

The following table shows the results of a survey of 420 authors by a (fictitious) publishing company: New Authors Established Authors Total Successful 90 10 100 Unsuccessful 150 170 320 Total 240 180 420 ​ A successful author is chosen at random. Compute the estimated probability of the event that the successful author is established.

Calculate the (theoretical) probability P ( E ), using the given information, assuming that all outcomes are equally likely. N(S) = 60 and n(E) = 12

A pair of dice is cast, and the number that appears uppermost on each die is observed. ​ Find the probability of the event that the sum of the numbers is 6.

According to a study conducted by the Harvard School of Public Health, a driver who was wearing a seatbelt was 31% 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 driver wearing a seatbelt, what is the probability that the airbag deployed in an accident in which the driver was killed (Round your answer to two decimal places.) The probability is __________.

A bag contains 6 red marbles, 3 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. Express your answer as a fraction in lowest terms.

In fall 2003, UCLA admitted 24% of its California resident applicants, 22% of its applicants from other U.S. states, and 18% of its international student applicants. Of all its applicants, 87% were California residents, 9% were from other U.S. states, and 4% were international students. What percentage of all admitted students were California residents (Round your answer to the nearest 1%.) The probability is __________%

Let W be the event that you will use the website tonight, Q be the event that your math grade will improve, and E be the event that you will use the website every night. Express the following event in symbols. "Either you will use the website every night, or your math grade will not improve."

This pie-chart shows the ethnic makeup of California schools in the 1981-1982 academic year. What is the probability that a randomly selected California student is neither White, nor Hispanic or Latino

The following table shows the results of a survey of authors by a (fictitious) publishing company: New Authors Established Authors Total Successful 5 25 30 Unsuccessful 15 55 70 Total 20 80 100 Consider the following events: S: An author is successful; U: An author is unsuccessful; N: An author is new; and E: An author is established. Are the events S and N mutually exclusive

Determine whether the given events A and B are independent, mutually exclusive, or neither. ​ A: Your new skateboard design is a success. B: Your new skateboard design is a failure.

Tommy the Dunker's performance on the basketball court is influenced by his state of mind: If he scores, he is twice as likely to score on the next shot as he is to miss, whereas if he misses a shot, he is four times as likely to miss the next shot as he is to score. If Tommy has missed a shot, what is the probability that he will score two shots later

Find the conditional probability of the event "The sum is 6, given that the green one is either 5 or 1" when two fair dice (one red and one green) are rolled.