Exam 8: Introduction to Probability

The following table gives the numbers of AIDS deaths in a single year for people over age 13 in various categories. Use the table to find the probability, rounded to four decimal places, that a person who died of AIDS in this year was Hispanic. ​ ​

A fair die is rolled. Find the probability that the result is a 4, given that the result is even. ​

From a deck of 52 playing cards, two cards are drawn, one after the other without replacement. What is the probability that the first will be a king and the second will be a jack of the same suit? ​

On June 16, 1997, two amateur golfers playing together hit back-to-back holes in one (Source: The Island Packet, June 19, 1997). Suppose the probability of an amateur golfer getting a hole-in-one is . If the golfers' shots are independent of each other, what is the probability that two amateur golfers will get back-to-back holes in one? ​

Each of urns I and II has 5 red balls, 2 white balls, and 3 green balls. Urn III has 5 red balls, 3 white balls, and 2 green balls. An urn is selected at random and a ball is drawn. If the ball is green G, find the probability that urn III was selected. ​

An examination consists of 11 questions. If 6 questions must be answered, find the number of different orders in which a student can answer the questions. ​

Find . ​

How many two-digit numbers can be formed from the digits 1, 3, 5, 7, 8, and 9 if each digit may be used repeatedly in each number? ​

Three balls are drawn, without replacement, from a bag containing 8 red balls and 6 white balls. Construct a probability tree to determine the probability that the third ball drawn is red R. ​

Six men and four women are semifinalists in a lottery. From this group, three finalists are to be selected by a drawing. What is the probability that all four finalists will be men? Round your answer to three decimal places. ​

A Markov chain has transition matrix and initial-probability vector . Find the probability vector for the third stage of the Markov chain. ​

An urn contains five red R balls numbered 1, 2, 3, 4 and 5, four white W balls numbered 6, 7, 8 and 9, and three black B balls numbered 10, 11 and 12. A ball is drawn from the urn. What is the probability that it is not black? ​

A senator asks his constituents to rank six issues in order of importance. How many rankings are possible? ​

How many three-digit numbers can be formed from the digits 1, 3, 5, 7, 8, and 9 if each digit can be used at most once in each number? ​

A car dealer has 7 different cars that he would like to display, but he has room to display only 4. In how many ways can he pick 4 cars to display? ​

A department store manager wants to display 4 brands of a product along one shelf of an aisle. In how many ways can he arrange the brands? ​

The following table gives the average number of voters in each of three political parties during the last 12 years, along with the average number that voted in presidential elections during this period. Use these data to find the probability, rounded to two decimal places, that a person selected at random from the registered Democratic voters will vote in the next election. ​ ​

A game of cards is played with a hand that consists of 3 cards dealt from a deck of 46 cards. How many different hands of cards are possible? ​

An unprepared student must take a 7-question, multiple-choice test that has 5 possible answers per question. If the student can eliminate 1 of the possible answers on the first 5 questions, and if she guesses on every question, what is the probability that she will answer every question incorrectly? ​

If the probability that event E will occur is , what is the probability that E will not occur? ​