Question

The probability that the next president will be a democrat is $1 / 2$, and the probability that the next president will be a woman is 0.3 , but the probability that the next president will be a woman and a democrat is just 0.1 . What is the probability that the next president will be democrat or a woman?

Name: Problem 3, Chapter 6: An Introduction to Decision Theory
Uploaded: 2022-04-04T01:51:38-08:00
Duration: 2 min 11 s
Channel: Gregory Higby
Description: The probability that the next president will be a democrat is 1 / 2, and the probability that the next president will be a woman is 0.3 , but the probability that the next president will be a woman and a democrat is just 0.1 . What is the probability that the next president will be democrat or a woman?

   The probability that the next president will be a democrat is $1 / 2$, and the probability that the next president will be a woman is 0.3 , but the probability that the next president will be a woman and a democrat is just 0.1 . What is the probability that the next president will be democrat or a woman?

An Introduction to Decision Theory

Martin Peterson 1st Edition

Chapter 6, Problem 3

Instant Answer

Solved by Expert Gregory Higby

04/04/2022

Step 1

The probability of the next president being a democrat is 1/2, and the probability of the next president being a woman is 0.3. So, the probability of the next president being a democrat or a woman is: P(democrat or woman) = P(democrat) + P(woman) - P(democrat Show more…

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The probability that the next president will be a democrat is $1 / 2$, and the probability that the next president will be a woman is 0.3 , but the probability that the next president will be a woman and a democrat is just 0.1 . What is the probability that the next president will be democrat or a woman?

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Key Concepts

Union of Events

This concept involves determining the probability that at least one of two events occurs. It requires considering all outcomes in either event, ensuring that any overlap between the events is properly managed to avoid counting the same outcome multiple times.

Inclusion-Exclusion Principle

This principle is used to calculate the probability of the union of events by adding the probabilities of individual events and then subtracting the probability of their intersection. It corrects for the overcounting of outcomes that are common to both events.

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