According to the Center for Disease Control and Prevention (CDC), up to 20% of Americans contract the influenza virus each year, and approximately 3% of all births in the United States result in birth defects each year.  Consider two randomly selected Americans and assume that these two randomly selected Americans are independent of each other.    The probability that neither of these two randomly selected Americans will contract the influenza virus in a given year is

It is estimated that 1% of the population has a certain genetic defect. A medical test is used to determine if people have this defect and, if a person has this defect, the test will correctly indicate this with probability 90%. However, if a person does not have this defect, the test will still indicate that he or she has the defect with probability 9.6%. If a person tests positive for this defect, what is the probability that the person actually has the defect? Express your answer, rounded to three decimal places, if necessary.

Assume that there is a 4% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. If copies of all your computer data are stored on three independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive? a. With two hard disk drives, the probability that catastrophe can be avoided is (Round to four decimal places as needed.) b. With three hard disk drives, the probability that catastrophe can be avoided is (Round to six decimal places as needed.)

Commercial fishermen in Alaska go into the Bering Sea to catch all they can of a particular species (salmon, herring, etc.) during a restricted season of a few weeks. The schools of fish move about in a way that is very difficult to predict, so the fishing in a particular spot might be excellent one day and terrible the next. The day-to-day records of catch size were used to discover that the probability of a good fishing day being followed by another good day is 0.5, by a medium day 0.3, and by a poor day 0.2. A medium day is most likely to be followed by another medium day, with a probability of 0.6, and equally like to be followed by a good or bad day. A bad day has a 0.3 probability of being followed by a good day, 0.2 of being followed by a medium day, and a 0.5 probability of being followed by another bad day. Construct a Markov chain model to describe the way the fishing days run. Referring to problem 1 in Chapter 2 (the fishing problem – reproduced below), calculate what you…

In the 2017 Seattle mayoral election, Ed Murray received 53.0% of the votes, Mike McGinn received 46.5% of the votes, and write-in candidates received the rest of the votes. Suppose we examine votes from randomly chosen people who voted in this election.   What is the probability that the first vote we examine is for Mike McGinn or for a write-in candidate?   Suppose we examine four randomly chosen votes. What is the probability that all four of the votes are for Ed Murray?   Suppose we examine four randomly chosen votes. What is the probability that none of the votes we examine is for Ed Murray?   Suppose we examine four randomly chosen votes. What is the probability that at least one of the votes we examine is for Ed Murray?

section 5.5   A personnel director has two lists of applicants for jobs. List 1 contains names of 24 women and 8 men, whereas List 2 contains the names of 9 women and 16 men. A name is randomly selected from List 1 and added to List 2. A name is then randomly selected from the augmented List 2. Given that the name selected is that of a man, what is the probability that a woman's name was originally selected from List 1? Round your answer to four decimal places, if necessary.

A drug test facility uses a test that has a 1% false negative rate, and a 2% false positive rate. It is estimated that 4% of the population is taking this drug. If a random person who tested positive is chosen, what is the probability that they are actually taking the drug?

In a recent senatorial election, 47% of the voters in a certain district were registered as Democrats, 36% were registered as Republicans, and 17% were registered as Independents. The incumbent Democratic senator was reelected over her Republican and Independent opponents. Exit polls indicated that she gained 73% of the Democratic vote, 22% of the Republican vote, and 34% of the Independent vote. Assuming that the exit poll is accurate, what is the probability that a vote for the incumbent was cast by a registered Republican? (Round your answer to three decimal places.)

Empirical evidence suggests that 25% of Florida drivers are uninsured. If four random Florida drivers are involved in an accident, what is the probability that more than one of them are uninsured?