4. Probability

In Exercises 19-22, determine whether the events are independent or dependent. Explain your reasoning.

19. Tossing a coin four times and getting four heads, and then tossing it a fifth time and getting a head

Manufacturing An assembly line produces 10,000 automobile parts. Twenty percent of the parts are defective. An inspector randomly selects 10 of the parts

b. Because the sample is only 0.1% of the population, treat the events as independent and use the binomial probability formula to approximate the probability that none of the selected parts are defective.

Finding New Music In Exercises 45–48, use the pie chart, which shows the results of a survey of 513 music listeners who were asked about their primary source for new music. (Source: The Sound of AI)

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47. You choose nine music listeners at random. What is the probability that none of them say their primary source for new music is friends or social media?

Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

27. Blood Types The probability that a person of Asian descent in the United States has type O+ blood is 39%. At random, six people of Asian descent in the United States are selected. (Source: American National Red Cross)

c. Find the probability that at least one of the six has type O+ blood.

Police Complaints The Chicago Tribune analyzed 17,713 complaints by citizens against Chicago police officers.

d. Of the 794 complaints with an affidavit that were found to be legitimate, 12 resulted in the officer being dismissed. Is it unusual for a legitimate complaint with an affidavit to result in the officer being dismissed?

[NW] Life Expectancy

The probability that a randomly selected 40-year-old male will live to be 41 years old is 0.99757, according to the National Vital Statistics Report, Vol. 56, No. 9.

a. What is the probability that two randomly selected 40-year-old males will live to be 41 years old

Driving under the Influence

Among 21- to 25-year-olds, 29% say they have driven while under the influence of alcohol. Suppose that three 21- to 25-year-olds are selected at random. Source: U.S. Department of Health and Human Services, reported in USA Today.

a. What is the probability that all three have driven while under the influence of alcohol?

Suppose that you roll a die 100 times and get six 80 times. Based on these results, what is the estimated probability that the next roll results in six?

"Blood TypesA person can have one of four blood types: A, B, AB, or O.

If a person is randomly selected, is the probability they have blood type A equal to 1/4? Why or why not?"

"More Genetics In Problem 29, we learned that for some diseases, such as sickle-cell anemia, an individual will get the disease only if he or she receives both recessive alleles. This is not always the case. For example, Huntington’s disease only requires one dominant gene for an individual to contract the disease. Suppose that a husband and wife, who both have a dominant Huntington’s disease allele (S) and a normal recessive allele (s), decide to have a child.

b. What is the probability that the offspring will not have Huntington’s disease? In other words, what is the probability that the offspring will have genotype ss? Interpret this probability.

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The word "and" in probability implies that we use the ______ Rule.

Suppose that events E and F are independent, P(E) = 0.3 and P(F) = 0.6. What is the P(E and F)?

Double Jackpot Shawn lives near the border of Illinois and Missouri. One weekend he decides to play \$1 in both state lotteries in hopes of hitting two jackpots. The probability of winning the Missouri Lotto is about 0.00000028357 and the probability of winning the Illinois Lotto is about 0.000000098239.

b. Find the probability that Shawn will win both jackpots.

Christmas Lights

Christmas lights are often designed with a series circuit. This means that when one light burns out the entire string of lights goes black. Suppose that the lights are designed so that the probability a bulb will last 2 years is 0.995. The success or failure of a bulb is independent of the success or failure of other bulbs.

a. What is the probability that in a string of 100 lights all 100 will last 2 years?

Earn More Than Your Parents?

In 1970, 92% of American 30-year-olds earned more than their parents did at age 30 (adjusted for inflation). In 2014, only 51% of American 30-year-olds earned more than their parents did at age 30. Source: Wall Street Journal, December 8, 2016.

b. What is the probability that two randomly selected 30-year-olds in 1970 earned more than their parents at age 30?