The table shows the results of a survey in which 3,545,286 public and 509,168 private school teachers were asked about their full-time teaching experience.

Are the events “being a public school teacher” and “having more than 20 years of full-time teaching experience” independent? Explain.

검증된 단계별 안내

Identify the two events: A = "being a public school teacher" and B = "having more than 20 years of full-time teaching experience."

Calculate the probability of event A, \(P(A)\), by dividing the total number of public school teachers by the total number of teachers surveyed: \(P(A) = \frac{3,545,286}{4,054,454}\).

Calculate the probability of event B, \(P(B)\), by dividing the total number of teachers with more than 20 years of experience by the total number of teachers surveyed: \(P(B) = \frac{936,268}{4,054,454}\).

Calculate the joint probability of both events occurring together, \(P(A \cap B)\), by dividing the number of public school teachers with more than 20 years of experience by the total number of teachers surveyed: \(P(A \cap B) = \frac{808,174}{4,054,454}\).

Check for independence by verifying if \(P(A \cap B) = P(A) \times P(B)\). If this equality holds, the events are independent; otherwise, they are dependent.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

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

Independence of Events

Two events are independent if the occurrence of one does not affect the probability of the other. Mathematically, events A and B are independent if P(A ∩ B) = P(A) × P(B). In this context, we check if being a public school teacher and having more than 20 years of experience occur independently.

Joint and Marginal Probabilities

Joint probability is the probability of two events happening together, while marginal probability is the probability of a single event regardless of the other. To test independence, we calculate the joint probability of both events and compare it to the product of their marginal probabilities.

Using Contingency Tables for Probability

Contingency tables display frequencies of categorical variables and help calculate probabilities. By dividing counts by the total sample size, we find probabilities for each category and their combinations, which are essential for testing independence between variables.

The table shows the results of a survey in which 3,545,286 public and 509,168 private school teachers were asked about their full-time teaching experience.Are the events “being a public school teacher” and “having more than 20 years of full-time teaching experience” independent? Explain.