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.

검증된 단계별 안내

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.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.