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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 3.2.6

True or False? In Exercises 5 and 6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.
6. If events A and B are dependent, then P(A and B) = P(A) · P(B).

검증된 단계별 안내
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Step 1: Begin by understanding the concept of dependent and independent events. Dependent events are those where the occurrence of one event affects the probability of the other. Independent events, on the other hand, do not influence each other.
Step 2: Recall the formula for the probability of the intersection of two events (A and B). For independent events, the formula is P(A and B) = P(A) · P(B). However, for dependent events, this formula does not hold because the probability of B depends on A.
Step 3: For dependent events, the correct formula is P(A and B) = P(A) · P(B|A), where P(B|A) is the conditional probability of B given that A has occurred.
Step 4: Compare the given statement, 'If events A and B are dependent, then P(A and B) = P(A) · P(B)', with the correct formula for dependent events. Notice that the statement is false because it uses the formula for independent events instead of the correct formula for dependent events.
Step 5: Rewrite the statement as a true statement: 'If events A and B are dependent, then P(A and B) = P(A) · P(B|A).' This correctly reflects the relationship between dependent events.

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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.

Dependent Events

Dependent events are two or more events where the occurrence of one event affects the probability of the other event(s). For example, drawing a card from a deck without replacement means the outcome of the first draw influences the probabilities of subsequent draws.
추천 영상:
05:54
Probability of Multiple Independent Events

Joint Probability

Joint probability refers to the probability of two events occurring simultaneously. For dependent events A and B, the joint probability is calculated differently than for independent events, as it takes into account the influence of one event on the other.
추천 영상:
5:37
Introduction to Probability

Independent Events

Independent events are those where the occurrence of one event does not affect the probability of the other event. For independent events A and B, the joint probability is given by P(A and B) = P(A) · P(B), which is not applicable for dependent events.
추천 영상:
05:54
Probability of Multiple Independent Events