- #1

Thecla

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- TL;DR Summary
- Probability of drawing white/black balls from a bag

In Aubrey Clayton's book" Bernoulli's Fallacy" which documents the conflict between frequentists and Bayesian interpretations of probability, he describes a problem that was proposed in the 19th century that gives a counterintuitive result.

The Problem:

"Infer the state of a bag of 3 balls each either black or white given that 2 successive white balls being drawn without replacement".

My first guess is the bag had 3 white balls or 2 white and one black ball,each equally possible. He says the answer is counterintuitive. The answer is not given, but what is the answer?

Dr. Clayton compares this problem to the problem first proposed by Martin Gardner in Scientific American(1959):

Mr. Smith says :I have 2 children and at least one of them is a boy. What is the probability that the other child is a boy?

The Problem:

"Infer the state of a bag of 3 balls each either black or white given that 2 successive white balls being drawn without replacement".

My first guess is the bag had 3 white balls or 2 white and one black ball,each equally possible. He says the answer is counterintuitive. The answer is not given, but what is the answer?

Dr. Clayton compares this problem to the problem first proposed by Martin Gardner in Scientific American(1959):

Mr. Smith says :I have 2 children and at least one of them is a boy. What is the probability that the other child is a boy?