Ch. 4 - Probability

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 4 - Probability

Problem 4.RE.7

Chapter 4, Problem 4.RE.7

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.

Verified step by step guidance

Step 1: Calculate the total number of study subjects by summing all the values in the table. Add the number of males and females who write with their left hand and those who do not.

Step 2: Determine the total number of subjects who write with their left hand by adding the 'Yes' values for males and females.

Step 3: Calculate the probability of selecting one subject who writes with their left hand. Divide the total number of left-handed subjects by the total number of study subjects. Use the formula: P(Left-Handed) = (Number of Left-Handed Subjects) / (Total Number of Subjects).

Step 4: Since the selection is with replacement, the probability of selecting two left-handed subjects is the product of the probabilities of selecting one left-handed subject twice. Use the formula: P(Both Left-Handed) = P(Left-Handed) × P(Left-Handed).

Step 5: Express the final probability in decimal form as required by the problem.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability

Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1. In this context, it refers to the chance of randomly selecting two individuals who both write with their left hand. The probability can be calculated using the formula P(A) = number of favorable outcomes / total number of outcomes.

Independent Events

Independent events are those whose outcomes do not affect each other. In this question, selecting one individual with replacement means that the first selection does not influence the second. Thus, the probability of both individuals being left-handed can be found by multiplying the probability of selecting a left-handed person in each trial.

Replacement in Sampling

Sampling with replacement means that after an individual is selected, they are returned to the population before the next selection. This ensures that the total number of individuals remains constant for each selection, allowing for consistent probability calculations. In this case, it affects how the probabilities are computed for the two selections.

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Related Practice

Textbook Question

Florida Pick 3 In the Florida Pick 3 lottery, you can place a “straight” bet of $1 by selecting the exact order of three digits between 0 and 9 inclusive (with repetition allowed), so the probability of winning is 1/1000. If the same three numbers are drawn in the same order, you collect $500, so your net profit is \$499.

a. Find the actual odds against winning.

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Textbook Question

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?

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Textbook Question

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?

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Textbook Question

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

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Textbook Question

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.

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Textbook Question

ATM You want to obtain cash by using an ATM, but it’s dark and you can’t see your card when you insert it. The card must be inserted with the front side up and the printing configured so that the beginning of your name enters first.

a. What is the probability of selecting a random position and inserting the card with the result that the card is inserted correctly?

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