4. Probability

Probability of a Girl Assuming that boys and girls are equally likely, find the probability of a couple having a boy when their third child is born, given that the first two children were both girls.

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

20. Coin and Die A coin is tossed and a die is rolled. Find the probability of tossing a tail and then rolling a number greater than 2.

In Exercises 1–10, use the data in the accompanying table and express all results in decimal form. (The data are from “The Left-Handed: Their Sinister History,” by Elaine Fowler Costas, Education Resources Information Center, Paper 399519.)

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Both Lefties If two of the study subjects are randomly selected with replacement, find the probability that they both write with their left hand.

In Exercises 9–20, use the data in the following table, which lists survey results from high school drivers at least 16 years of age (based on data from “Texting While Driving and Other Risky Motor Vehicle Behaviors Among U.S. High School Students,” by O’Malley, Shults, and Eaton, Pediatrics, Vol. 131, No. 6). Assume that subjects are randomly selected from those included in the table. Hint: Be very careful to read the question correctly.

Texting and Alcohol If one of the high school drivers is randomly selected, find the probability that the selected driver did not text while driving and did not drive when drinking.

In Exercises 6–10, use the following results from tests of an experiment to test the effectiveness of an experimental vaccine for children (based on data from USA Today). Express all probabilities in decimal form.

Find the probability of randomly selecting 2 subjects without replacement and finding that they both developed flu.

If P(E) = 0.6 and P(E|F) = 0.34, are events E and F independent?

[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

Redundancy in Computer Hard Drives It is generally recognized that it is wise to backup computer data. Assume that the following refer to use of Western Digital model WD60EFRX hard drives, which have an annual failure rate of 3.66% (based on data from Backblaze, Inc.).

a. If you store all of your computer data on a single hard drive, what is the probability that the drive will fail during a year?

Surge Protectors Refer to the accompanying figure showing surge protectors p and q used to protect an expensive television. If there is a surge in the voltage, the surge protector reduces it to a safe level. Assume that each surge protector has a 0.985 probability of working correctly when a voltage surge occurs.

c. Which arrangement should be used for better protection?

In Exercises 9–20, use the data in the following table, which lists survey results from high school drivers at least 16 years of age (based on data from “Texting While Driving and Other Risky Motor Vehicle Behaviors Among U.S. High School Students,” by O’Malley, Shults, and Eaton, Pediatrics, Vol. 131, No. 6). Assume that subjects are randomly selected from those included in the table. Hint: Be very careful to read the question correctly.

Texting and Alcohol If four different high school drivers are randomly selected, find the probability that they all texted while driving.

According to Bayes’ Theorem, the probability of event A , given that event B has occurred, is

P(A|B) = P(A) * P(B|A)P(A) * P(B|A) + P(A') * P(B|A').

In Exercises 33–38, use Bayes’ Theorem to find P(A|B).

33. P(A) = 2/3, P(A') = 1/3, P(B|A) = 1/5 , and P(B|A') = 1/2

Classifying Events Based on Studies In Exercises 15-18, identify the two events described in the study. Do the results indicate that the events are independent or dependent? Explain your reasoning.

17. A study found that there is no relationship between playing violent video games and aggressive or bullying behavior in teenagers. (Source: The Royal Society Publishing)

Bowling

Suppose that Ralph gets a strike when bowling 30% of the time.

a. What is the probability that Ralph gets two strikes in a row?

Rolling a Die What is the probability of obtaining 4 ones in a row when rolling a fair, six-sided die? Interpret this probability.