Exam 7: Probability: Living With the Odds

Use the at least once rule to find the indicated probability. -In a blood testing procedure, blood samples from 5 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative. If the probability that an Individual sample tests positive is 0.08, what is the probability that the mixture will test positive?

Solve the problem. -The table shows the prizes and probabilities of winning (on a single $1 ticket)for a particular state lottery. How much would you expect to win or lose if you bought one $1 ticket every day for a year? Round to the nearest dollar.

Solve the problem. Round your answer to 2 decimal places when necessary. -A U.S. city with a population of 1.7 million reports 35,738 births. What is the birth rate in births per 1000 people?

Solve the problem. Round your answer to 2 decimal places when necessary. -The population of a certain country is about 132 million. The overall birth rate is 14.3 births per 1000. Approximately how many births were there in the country?

Find the expected value. -A commercial building contractor is trying to decide which of two projects to commit her company to. Project A will yield a profit of $50,000 with a probability of 0.6, a profit of $86,000 with a Probability of 0.3, and a profit of $10,000 with a probability of 0.1. Project B will yield a profit of $100,000 with a probability of 0.1, a profit of $69,000 with a Probability of 0.7, and a loss of $20,000 with a probability of 0.2. Find the expected profit for each project. Based on expected values, which project should the Contractor choose?

Solve the problem. -How many different 4-letter radio-station call letters can be made if the first letter must be K or W, repeats are allowed, but the call letters cannot end in an O?

Find the expected value. -You are given 16 to 1 odds against tossing 4 tails in 4 tosses of a fair coin. This means that you win $16 if you succeed and you lose $1 if you fail. Find the expected value (to you)of the game. Round To the nearest cent.

Find the indicated probability. Round your answer to 6 decimal places when necessary. -Two cards are selected without replacement from a standard deck of 52 cards. What is the probability that both cards are the same color (i.e.either both black or both red)?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that either doubles are rolled or the sum of the dice is 6.

Solve the problem. -A singer-songwriter wishes to compose a melody. Each note in the melody must be one of the 20 notes in her vocal range. How many different sequences of 5 notes are possible?

Solve the problem. -In a certain lottery, 6 different numbers between 1 and 9 inclusive are drawn at random. These are the winning numbers. If you choose 6 different numbers at random between 1 and 9, what is the probability you will match the winning numbers? Assume that the order of the numbers is Unimportant.

Provide an appropriate response. -In a large casino, the house wins on its blackjack games with a probability of 50.7%. Which of the following events is the most unlikely? A: You win at a single game. B: You come out ahead after playing forty times. C: You win at a single game given that you have just won ten games in a row. D: You win at a single game given that you have just lost ten games in a row.

Find the indicated probability. Round your answer to 6 decimal places when necessary. -You are dealt two cards successively (without replacement)from a shuffled deck of 52 playing cards. Find the probability that both cards are black.

Find the indicated probability. -The following table displays the number of siblings for students at one middle school. Find the probability that a randomly selected student in the school has 2 siblings. Round your answer to the Nearest thousandth. Number of siblings Frequency 0 189 1 246 2 124 3 58 4 25 5 10 6 6 7 3

Find the indicated probability. -The table below describes the smoking habits of a group of asthma sufferers. If one of the 979 subjects is randomly selected, find the probability that the person chosen is a nonsmoker and a woman. Round your answer to the nearest thousandth when necessary.

Determine whether the events A and B are independent. -Two cards are selected at random from a standard deck of 52 cards without replacement. Event A: An ace is selected on the first draw Even B: An ace is selected on the second draw

Use the relative frequency method to estimate the probability. Round your answer to 2 decimal places when necessary. -You count 58 heads when you toss a coin 100 times. If you don't know whether the coin is fair, what is the probability that the next toss will be heads?

Provide an appropriate response. -An insurance company sells an insurance policy for $1000. If there is no claim on a policy, the company makes a profit of $1000. If there is a claim on a policy, the company faces a large loss on That policy. The expected value to the company, per policy, is $250. Which of the following statements is (are)true? A: The most likely outcome on any single policy is a profit for the company of $\$ 250$ . B: If the company sells only a few policies, its profit is hard to predict. C: If the company sells a large number of policies, the average profit per policy will be close to \$250.

Solve the problem. Round your answer to 2 decimal places when necessary. -A U.S. city with a population of 2.2 million reports 30,724 births in one year. How many people are born per day in the city?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -Three fair coins are tossed. Find the probability of getting the same thing on all three coins.