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Ch. 3 - Probability
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 3 - ProbabilityProblema 3.CR.14c
Capitolo 3, Problema 3.CR.14c

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.
Table showing teaching experience of public and private school teachers with counts across four experience ranges and totals.
Are the events “being a public school teacher” and “having more than 20 years of full-time teaching experience” independent? Explain.

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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.

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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.
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Probability of Multiple Independent Events

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.
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Introduction to Probability

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.
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Contingency Tables & Expected Frequencies
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