Similar puzzles with different answers

  • Context: Undergrad 
  • Thread starter Thread starter bob j
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around two probability puzzles that appear similar but yield different answers. The first puzzle involves selecting a pancake from a hat with varying colors on each side, while the second puzzle concerns the genders of two children when one is observed to be a boy. The focus is on understanding the underlying probability principles and reasoning behind the differing outcomes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant asserts that the pancake problem yields a probability of 2/3 for the other side being brown, based on the distribution of brown sides among the pancakes.
  • Another participant argues that the child problem results in a probability of 1/2 for both children being boys, as knowing one child's gender provides no information about the other without additional context.
  • A participant requests a mathematical derivation to clarify why the two scenarios are not equivalent in terms of probability.
  • One participant emphasizes that the pancake problem allows for a clear understanding of the probabilities involved due to the known quantities of each side, while the child problem lacks this clarity.

Areas of Agreement / Disagreement

Participants generally agree that the two problems are different in nature, but there is ongoing debate about the reasoning behind the probabilities and the implications of the information provided in each scenario.

Contextual Notes

Participants express uncertainty about the equivalence of the two problems and the implications of the information given in each case, highlighting the need for a deeper mathematical understanding of the scenarios.

bob j
Messages
22
Reaction score
0
I have a question about two puzzles that seem similar to me, but I have different answers to them.

One is the following:
You have a hat in which there are three pancakes: One is golden on both sides, one is brown on both sides, and one is golden on one side and brown on the other. You withdraw one pancake, look at one side, and see that it is brown. What is the probability that the other side is brown?

The answer is 2/3 and uses the fact that you had twice as much of probability of choosing the pancake with double brown.

The other problem is this:
Ms. X has two children. You see her walking with one of her children and that child is a boy. What is the probability that both children are boys?
I found this on a book and the answer was 1/2.

Are these different problems? They look the same to me

Thanks
 
Physics news on Phys.org
These are different problems. In one case, you know how many golden and brown pancake sides there are. Finding a brown one gives you information about which pancake you picked. In the other case, you have no idea what the genders of the two children are, so the gender of one gives no information about the gender of the other. If you knew there was one boy and one girl, or two boys, you would be able to say the gender of the one not present with certainty, but you don't have this information, so information about one says nothing about the other.
 
could you possibly tell me how to derive that mathematically? It is not clear to me why knowing one side of the pancake is brown is not equivalent to knowing that one child is a boy.

Thanks a lot
 
For the pancake problem, I'm equally likely to pick any side of any pancake. I picked a brown side. There are three brown sides, two of them on the all brown pancake, one on the half brown one. The odds that I picked the all brown pancake then must be 2/3.

For the other case, knowing one kid is a boy, that gives me no information about the other one since I don't know the total numbers.
 

Similar threads

Undergrad What Is the Counterintuitive Probability in the Bag of Balls Problem?
  • · Replies 18 ·
Replies
18
Views
4K
Undergrad Probability of 2 Different Gendered Children Born in Order
  • · Replies 10 ·
Replies
10
Views
5K
Graduate What is the probability that the top pancake is burned on both sides?
  • · Replies 21 ·
Replies
21
Views
12K
MHB Could use help, know the answers but with the process and equations
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Calculating the odds of drawing 3 "no" notes from a hat with 3 "no" and 3 "yes" notes
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad A variation of the sleeping beauty problem
  • · Replies 57 ·
2
Replies
57
Views
7K
Graduate A game of seemingly mutually independent events
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Please Explain (actually explain) The Monty Hall Problem
  • · Replies 131 ·
5
Replies
131
Views
9K
High School Boy/girl riddle (conditional probability)
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Adding random numbers: Tolerance analysis
  • · Replies 11 ·
Replies
11
Views
4K