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Ch. 3 - Probability
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470당신이 사용하는 게 아니라요?교과서 변경
3장, 문제 3.3.16

16. Can Defects Of the cans produced by a company, 96% do not have a puncture, 93% do not have a smashed edge, and 89.3% have neither a puncture nor a smashed edge. Find
the probability that a randomly selected can does not have a puncture or a smashed edge.

검증된 단계별 안내
1
Step 1: Define the events. Let A represent the event that a can does not have a puncture, and B represent the event that a can does not have a smashed edge. The probabilities given are P(A) = 0.96, P(B) = 0.93, and P(A ∩ B) = 0.893.
Step 2: Recall the formula for the union of two events. The probability that a can does not have a puncture or a smashed edge is given by P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
Step 3: Substitute the given probabilities into the formula. Replace P(A) with 0.96, P(B) with 0.93, and P(A ∩ B) with 0.893 in the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
Step 4: Simplify the expression. Add P(A) and P(B), then subtract P(A ∩ B) to calculate P(A ∪ B).
Step 5: Interpret the result. The value of P(A ∪ B) represents the probability that a randomly selected can does not have a puncture or a smashed edge.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
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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 helps quantify the chances of a can being free from defects, such as punctures or smashed edges. Understanding how to calculate probabilities is essential for solving the question.
추천 영상:
가이드 코스
5:37
Introduction to Probability

Complement Rule

The Complement Rule states that the probability of an event not occurring is equal to 1 minus the probability of the event occurring. This concept is crucial for determining the probability of a can not having a puncture or a smashed edge by using the given probabilities of the defects.
추천 영상:
가이드 코스
4:23
Complementary Events

Union of Events

The Union of Events refers to the probability that at least one of multiple events occurs. In this case, it involves calculating the probability that a can has either a puncture or a smashed edge. Understanding how to combine probabilities of different events is key to finding the solution.
추천 영상:
가이드 코스
05:54
Probability of Multiple Independent Events