4. Probability

Boy or Girl? In Exercises 71-74, a couple plans to have three children. Each child is equally likely to be a boy or a girl.

74. What is the probability that at least one child is a boy?

Language: Complement of “At Least One” Let A=the event of getting at least one defective calculator when four are randomly selected with replacement from a batch. Write a statement describing event A

Composite Drug Test Based on the data in Table 4-1, assume that the probability of a randomly selected person testing positive for drug use is 0.126. If drug screening samples are collected from 5 random subjects and combined, find the probability that the combined sample will reveal a positive result. Is that probability low enough so that further testing of the individual samples is rarely necessary?

Finding the Probability of the Complement of an Event The age distribution of the residents of Ithaca, New York, is shown at the left. In Exercises 59-62, find the probability of the event. (Source: U.S. Census Bureau)

61. Event C: A randomly chosen resident of Ithaca is not less than 18 years old.

Finding the Probability of the Complement of an Event In Exercises 17-20, the probability that an event will happen is given. Find the probability that the event will not happen.

19. P(E)=0.03

Finding the Probability of an Event In Exercises 21-24, the probability that an event will not happen is given. Find the probability that the event will happen. 

21. P(E') =0.95

In Problems 5–12, a probability experiment is conducted in which the sample space of the experiment is S={1,2,3,4,5,6,7,8,9,10,11,12}S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}S={1,2,3,4,5,6,7,8,9,10,11,12}. Let event E={2,3,4,5,6,7}E = \{2, 3, 4, 5, 6, 7\}E={2,3,4,5,6,7}, event F={5,6,7,8,9}F = \{5, 6, 7, 8, 9\}F={5,6,7,8,9}, event G={9,10,11,12}G = \{9, 10, 11, 12\}G={9,10,11,12}, and event H={2,3,4}H = \{2, 3, 4\}H={2,3,4}. Assume that each outcome is equally likely.

List the outcomes in Fc. Find P(Fc).

Writing In Exercises 89 and 90, write a statement that represents the complement of the probability.

90. The probability of randomly choosing a car with more than one cause for showing its "CHECK ENGINE" light from the population of vehicles showing "CHECK ENGINE" lights.

Blue Eyes Assume that 35% of us have blue eyes (based on a study by Dr. P. Soria at Indiana University).

b. Find the value of P(B_bar).

Redundancy in Computer Hard Drives The Seagate ST8000NM0055 hard drive has a 1.22% rate of failures in a year (based on data from Backblaze, Inc.). For the following, assume that all hard drives are that Seagate model.

a. If all of your computer data are 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? Express the result with six decimal places.

Telephone Numbers The telephone numbers for a region of Pennsylvania have an area code of 570. The next seven digits represent the local telephone numbers for that region. These cannot begin with a 0 or 1. In Exercises 15 and 16, assume your cousin lives within the given area code.

16. What is the probability of not randomly generating your cousin's telephone number on the first try?

Women in Movies In a recent year, speaking characters in movies were 68.2% male. What is the probability of randomly selecting a character with a speaking part and getting a female? What should be the value of that probability?

Marijuana Use The percent distribution of the last marijuana use (either medical or nonmedical) for a sample of 13,373 college students is shown in the pie chart. Find the

probability of each event. (Source: American College Health Association)

d. Randomly selecting a student who has not used marijuana within the last 12 months

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.)

Complement If L represents the event of randomly selecting one of the study subjects and getting someone who writes with their left hand, what does L represent? Find the value of P(L)

In Exercises 35–38, the bar graph shows the results of a survey in which 8806 undergraduate students were asked how many hours they spend on studying and other academic activities outside of class in a typical week. (Source: American College Health Association)

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37. Find the probability of randomly selecting an undergraduate who does not study from 6 to 10 hours per week.