Exam 8: Probability

It snows in Greenland an average of once in 20 days, and when it does, glaciers have a 25% chance of growing. When it does not snow in Greenland, glaciers have only a 5% chance of growing. What is the probability that it is snowing in Greenland when glaciers are growing Please, round your answer to four decimal places.

In 2003, 43.8% of all light vehicles were cars, 28.1% were pickups, and 28.1% were 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 an SUV Please, round your answer to three decimal places, if necessary. Light Truck 210 SUV 371 Cars 1.000

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 5 212 1,124 2,882 5,258 9,481 Not Admitted 687 3,506 9,860 12,230 5,150 31,433 Total Applicants 692 3,718 10,984 15,112 10,408 40,914 ​ Enter your answer in decimal form, not as a fraction. The probability is __________.

In a (fictitious) soccer tournament involving the four teams San Diego State, De Paul, Colgate, and Hofstra, find the probability that Hofstra will play Colgate in the finals and lose. (Assume that all outcomes are equally likely and that the teams not listed in the first round slots are placed at random.) ​

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

According to a study in The New England Journal of Medicine, 202 of a sample of 5,990 middle-aged men had developed diabetes. It also found that men who were very active (burning about 3,500 calories daily) were half as likely to develop diabetes compared with men who were sedentary. Assume that one-fourth of all middle-aged men are very active, and the rest are classified as sedentary. What is the probability that a middle-aged man with diabetes is very active Please, round your answer to two decimal places.

Suzy grabs four marbles from a bag containing three white marbles and six blue marbles. Find the probability that two of the marbles are white, and two are blue.

My couch potato friend enjoys sitting in front of the TV and grabbing handfuls of five chocolates at random from his snack jar. Unbeknownst to him, I have replaced 1 of the twelve chocolates in his jar with a cashew. (He hates cashews with a passion!) How many possible outcomes are there the first time he grabs five chocolates How many of these include the cashew

You are given a transition matrix P and initial distribution vector v. Find the two-step transition matrix and the distribution vector after two steps. $P = \left[ \begin{array} { c c } 0 & 1 \\\frac { 1 } { 3 } & \frac { 2 } { 3 }\end{array} \right]$ , $v = \left[ \begin{array} { l l } \frac { 1 } { 4 } & \frac { 3 } { 4 }\end{array} \right]$

New York Times survey of needy and disabled youths showed that 51% of those who had no preschool education were arrested or charged with a crime by the time they were 19, whereas only 31% who had preschool education wound up in this category. The survey did not specify what percentage of the youths in the survey had preschool education, so let us take a guess at that and estimate that 25% of them had attended preschool. What percentage of the youths arrested or charged with a crime had no preschool education Round your answer to the nearest 0.01%. The answer is __________% What would this figure be if 75% of the youths had attended preschool Round your answer to the nearest 0.01%. The answer is __________% Would youths who had preschool education be more likely to be arrested or charged with a crime than those who did not

Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round the answer to four decimal places. ​ $Y _ { 1 }$ , $Y _ { 2 }$ , $Y _ { 3 }$ form a partition of S. ​ $P \left( X \mid Y _ { 1 } \right) = 0.2$ , $P \left( X \mid Y _ { 2 } \right) = 0.2$ , $P \left( X \mid Y _ { 3 } \right) = 0.6$ , $P \left( Y _ { 1 } \right) = 0.3$ , $P \left( Y _ { 2 } \right) = 0.4$ . ​ Find $P \left( Y _ { 1 } \mid X \right)$ . ​ $P \left( Y _ { 1 } \mid X \right) =$ __________

Find the conditional probability of the event "The red one is 5, given that the sum is 7" when two fair dice (one red and one green) are rolled.

The following table shows the results of a survey of 420 authors by a (fictitious) publishing company: New Authors Established Authors Total Successful 70 50 120 Unsuccessful 130 170 300 Total 200 220 420 ​ An author is chosen at random. Compute the estimated probability of the event that the author is established and successful.

In 1998, 86% of all Caucasians in the U.S., 77% of all African-Americans, 70% 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 Round your answer to the nearest 1%.

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 6 212 1,128 2,882 5,267 9,495 Not Admitted 681 3,508 8,798 12,230 5,150 30,367 Total Applicants 687 3,720 9,926 15,112 10,417 39,862

If $P ( A \cap B ) = 0.11$ , $P ( A \cup B ) = 0.42$ , and $P ( B ) = 0.27$ , then find $P ( A )$ .

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. Employed Unemployed Not in Labor Force Total Less Than 4 Years High School 11.5 0.9 10.4 22.8 More than 4 Years High School 69 3 21.4 93.4 Total 80.5 3.9 31.8 116.2 ​ Find the probability that a person was employed, given that the person has competed less than 4 years of high school. Please round the answer to two decimal places.

According to a New York Times/CBS poll released in March, 2005, 78% agreed that it should be the government's responsibility to provide a decent standard of living for the elderly, and 41% agreed that it would be a good idea to invest part of their Social Security taxes on their own. If agreement with one of these propositions is independent of agreement with the other, what is the probability that a person agreed with both propositions (Round your answer to two decimal places.)

In 2001, 37.4% 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

A bag contains 4 red marbles, 4 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 has 2 red ones and 1 of each of the other colors. Express your answer as a fraction in lowest terms.