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.

Verified step by step guidance

1. Step 1: Understand the problem. We are tasked with finding the probability of randomly selecting a study subject who either writes with their left hand or is a female. This involves using the formula for the union of two events: P(A or B) = P(A) + P(B) - P(A and B).
2. Step 2: Calculate the total number of study subjects. Add all the values in the table: Total = 23 (Male Left-Handed) + 217 (Male Right-Handed) + 65 (Female Left-Handed) + 455 (Female Right-Handed).
3. Step 3: Calculate P(A), the probability of selecting someone who writes with their left hand. Add the number of left-handed males and females (23 + 65), then divide by the total number of study subjects.
4. Step 4: Calculate P(B), the probability of selecting someone who is female. Add the number of females (65 + 455), then divide by the total number of study subjects.
5. Step 5: Calculate P(A and B), the probability of selecting someone who is both female and writes with their left hand. This is simply the number of left-handed females (65) divided by the total number of study subjects. Finally, use the formula P(A or B) = P(A) + P(B) - P(A and B) to find the desired probability.

Key Concepts

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it involves calculating the chance of randomly selecting a subject who either writes with their left hand or is female. The formula for probability is the number of favorable outcomes divided by the total number of possible outcomes.

Union of Events

The union of events refers to the occurrence of at least one of two or more events. In this question, we are interested in the union of two events: selecting someone who writes with their left hand and selecting a female. The probability of the union can be calculated using the formula P(A or B) = P(A) + P(B) - P(A and B), where A and B are the two events.

Data Representation

Data representation involves organizing and displaying data in a way that makes it easy to analyze and interpret. In this case, the data is presented in a contingency table that categorizes subjects based on gender and whether they write with their left hand. Understanding how to read and interpret this table is crucial for calculating the required probabilities.