Combination Lock The typical combination lock uses three numbers, each between 0 and 49. Opening the lock requires entry of the three numbers in the correct order. Is the name “combination” lock appropriate? Why or why not?

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?

Soccer Shootout In the FIFA Women’s World Cup 2019, a tie at the end of two overtime periods leads to a “shootout” with five kicks taken by each team from the penalty mark. Each kick must be taken by a different player. How many ways can 5 players be selected from the 11 eligible players? For the 5 selected players, how many ways can they be designated as first, second, third, fourth, and fifth?

DNA Nucleotides DNA (deoxyribonucleic acid) is made of nucleotides. Each nucleotide can contain any one of these nitrogenous bases: A (adenine), G (guanine), C (cytosine), T (thymine). If one of those four bases (A, G, C, T) must be selected three times to form a linear triplet, how many different triplets are possible? All four bases can be selected for each of the three components of the triplet.

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.

In Exercises 33–40, use the given probability value to determine whether the sample results are significant.

Voting Repeat the preceding Exercise 33 after replacing 40 Democrats being placed on the first line of voting ballots with 26 Democrats being placed on the first line. The probability of getting a result as high as 26 is 0.058638.

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 or Drinking If one of the high school drivers is randomly selected, find the probability of getting one who texted while driving or drove when drinking alcohol.

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?

Shared Birthdays Find the probability that of 25 randomly selected people, at least 2 share the same birthday.

In Exercises 13–20, express the indicated degree of likelihood as a probability value between 0 and 1.

Randomness When using a computer to randomly generate the last digit of a phone number to be called for a survey, there is 1 chance in 10 that the last digit is zero

California Lottery Let A denote the event of placing a $1 straight bet on the California Daily 4 lottery and winning. There are 10,000 different ways that you can select the four digits (with repetition allowed) in this lottery, and only one of those four-digit numbers will be the winner. What is the value of P(A)? What is the value of P(Abar)?

Notation For a polygraph (lie detector) used when a subject is presented with a question, let L= the subject lied and let Y = the polygraph indicated that the subject told a lie. Use your own words to translate the notation P (Y|L) into a verbal statement.

In Exercises 29–32, use the given sample space or construct the required sample space to find the indicated probability.

Three Children Use this sample space listing the eight simple events that are possible when a couple has three children (as in Example 2): {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}. Assume that boys and girls are equally likely, so that the eight simple events are equally likely. Find the probability that when a couple has three children, there is exactly one girl.

Simulating Dice When two dice are rolled, the total is between 2 and 12 inclusive. A student simulates the rolling of two dice by randomly generating numbers between 2 and 12. Does this simulation behave in a way that is similar to actual dice? Why or why not?

Computer Variable Names A common computer programming rule was that names of variables must be between one and eight characters long. The first character can be any of the 26 letters, while successive characters can be any of the 26 letters or any of the 10 digits. For example, allowable variable names include A, BBB, and M3477K. How many different variable names are possible? (Ignore the difference between uppercase and lowercase letters.)

Mendel’s Peas Mendel conducted some of his famous experiments with peas that were either smooth yellow plants or wrinkly green plants. If four peas are randomly selected from a batch consisting of four smooth yellow plants and four wrinkly green plants, find the probability that the four selected peas are of the same type.

Same Birthdays If 25 people are randomly selected, find the probability that no 2 of them have the same birthday. Ignore leap years.

Jumble Many newspapers carry “Jumble,” a puzzle in which the reader must unscramble letters to form words. The letters MHRHTY were included in newspapers on the day this exercise was written. How many ways can those letters be arranged? Identify the correct unscrambling, then determine the probability of getting that result by randomly selecting one arrangement of the given letters.

In Exercises 33–40, use the given probability value to determine whether the sample results are significant.

Voting Repeat Exercise 33 after replacing 40 Democrats being placed on the first line of voting ballots with 14 Democrats being placed on the first line. The probability of getting a result as low as 14 is 0.029792.

In Exercises 13–20, express the indicated degree of likelihood as a probability value between 0 and 1.

SAT Test When making a random guess for an answer to a multiple choice question on an SAT test, the possible answers are a, b, c, d, e, so there is 1 chance in 5 of being correct.

In Exercises 13–20, express the indicated degree of likelihood as a probability value between 0 and 1.

Square Peg Sydney Smith wrote in “On the Conduct of the Understanding” that it is impossible to fit a square peg in a round hole.

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.

Heights of Presidents Theories have been developed about the heights of winning candidates for the U.S. presidency and the heights of candidates who were runners up. Listed below are heights (cm) from recent presidential elections. Construct a graph suitable for exploring an association between heights of presidents and the heights of the presidential candidates who were runners-up. What does the graph suggest about that association?

Cloud Seeding The “Florida Area Cumulus Experiment” was conducted by using silver iodide to seed clouds with the objective of increasing rainfall. For the purposes of this exercise, let the daily amounts of rainfall be represented by units of rnfl. (The actual rainfall amounts are in or )

Find the value of the following statistics and include appropriate units based on rnfl as the unit of measurement.

15.53 7.27 7.45 10.39 4.70 4.50 3.44 5.70 8.24 7.30 4.05 4.46

a. mean

b. median

Sampling Eye Color Based on a study by Dr. P. Sorita Soni at Indiana University, assume that eye colors in the United States are distributed as follows: 40% brown, 35% blue, 12% green, 7% gray, 6% hazel.

a. A statistics instructor collects eye color data from her students. What is the name for this type of sample?

Cloud Seeding The “Florida Area Cumulus Experiment” was conducted by using silver iodide to seed clouds with the objective of increasing rainfall. For the purposes of this exercise, let the daily amounts of rainfall be represented by units of rnfl. (The actual rainfall amounts are in or )

Find the value of the following statistics and include appropriate units based on rnfl as the unit of measurement.

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c. midrange

d. range

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.)

Lefty or Female Find the probability of randomly selecting one of the study subjects and getting someone who writes with their left hand or is a female.

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.)

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

Vision Correction About 75% of the U.S. population uses some type of vision correction (such as glasses or contact lenses).

b. If four different people are randomly selected, what is the probability that they all use vision correction?

Is the Researcher Cheating? You become suspicious when a genetics researcher “randomly” selects numerous groups of 20 newborn babies and seems to consistently get 10 girls and 10 boys. The researcher claims that it is common to get 10 girls and 10 boys in such cases.

a. If 20 newborn babies are randomly selected, how many different gender sequences are possible?