Exam 7: Introduction to Probability

Suppose a die is biased (unfair) so that each odd-numbered face has probability of resulting, and each even face has probability of resulting. Find the probability of getting a number greater than 1. ​

Forty-eight percent of the U.S. population is female, and 23.3% of the female population have a college degree. If a U.S. resident is chosen at random, what is the probability, to three decimal places, that the person is a female with a college degree? ​

How many four-digit numbers can be formed from the digits 1, 3, 5, 7, 8, and 9 if the numbers are less than 9,000 and digits are not used repeatedly? (Hint: Begin with the digit where there is a restriction on the choices.) ​

What is the probability of being dealt a poker hand of 5 cards containing exactly 4 spades? Round your answer to two decimal places. ​

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

An urn contains five red balls numbered 1, 2, 3, 4 and 5, four white balls numbered 6, 7, 8 and 9, and three black balls numbered 10, 11 and 12. A ball is drawn from the urn. What is the probability that it is an odd-numbered ball O? ​

In how many ways can a hand consisting of 3 spades, 3 hearts, 2 clubs, and 1 diamond be selected from a deck of 52 cards? ​

A small town has 8500 adult males and 5500 adult females. A sociologist conducted a survey and found that 40% of the males and 30% of the females drink heavily. An adult is selected at random from the town. What is the probability, rounded to four decimal places, that the person drinks heavily DH? ​

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? ​

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 female or Hispanic. ​

Use the transition matrix and initial probability vector to find the resulting third probability vector. Round all numerical values in your answer to three decimal places. ​

Find the probability of being dealt a hand containing 5 spade, 10 hearts, 9 diamonds, and 6 clubs. Assume that a normal deck of 52 cards is used. Round your answer to four decimal places. ​

Suppose an ice cream store offers 34 flavors of ice cream cones in sizes small, medium, and large. If four toppings are available to put on a cone, and a cone can be bought without a topping, how many different selections of ice cream are available if each cone has one flavor and one or no toppings? ​

If 11 people are qualified for the next flight to a space station, how many different groups of 3 people can be chosen for the flight? ​

A box of 22 transistors contains 6 that are defective. If 2 transistors are drawn from the box together, what is the probability that exactly one of the two transistors is defective? Round your answer to four decimal places. ​

A retailer purchases 140 of a new brand of DVD player, of which 4 are defective. The purchase agreement says that if he tests 8 chosen at random and finds 1 or more defective, he receives all the DVD players free of charge. What is the probability that he will not have to pay for the DVD players? Round your answer to three decimal places. ​

A fair die is thrown twice. What is the probability that a 3 will result the first time and a 2 the second time? ​

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 female. ​ ​

If 5% of all light bulbs a company manufactures are defective, the probability of any one bulb being defective is 0.05. What is the probability that two bulbs drawn independently from the company's stock will be defective? Round your answer to eight decimal places. ​

A bag contains 7 white balls and 8 red balls. Three balls are drawn, without replacement, from the bag. Construct a probability tree to determine the probability that exactly one white W ball is drawn. ​