All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Probability
2 coins (Posted on 2016-03-18) Difficulty: 3 of 5
Suppose you have 2 identical-looking coins: one that is fair and one that comes up heads 75% of the time.
You randomly chose one of them, flip it 3 times and it comes up as H-H-T.

What is the chance that the coin you picked is the fair one?

Source: Project Euler

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Bayes Comment 2 of 2 |
The probability that you would pick the fair coin and it would come up HHT is 1/2 * 1/8 = 1/16.

The probability that you would pick the biased coin and it would come up HHT is 1/2 * (3/4)^2 * 1/4 = 9/128.

By Bayes' rule/theorem, the probability that you did pick the fair coin given this outcome, is (1/16) / (1/16 + 9/128) = 8/17.



or, in 128 trials with exact regard to probabilities, 8 out of 17 cases of HHT were from the fair coin:




  fair HHH
  fair HHH
  fair THH
  fair THH
  fair HHH
  fair HHH
  fair TTH
  fair TTH
  fair HTH
  fair HTH
  fair TTH
  fair TTH
  fair HTH
  fair HTH
  fair THH
  fair THH
  fair HHH
  fair HHH
  fair THH
  fair THH
  fair HHH
  fair HHH
  fair TTH
  fair TTH
  fair HTT
  fair HTT
  fair TTT
  fair TTT
  fair HTT
  fair HTT
  fair THT
  fair THT
  fair HHT *
  fair HHT *
  fair THT
  fair THT
  fair HHT *
  fair HHT *
  fair TTT
  fair TTT
  fair HTT
  fair HTT
  fair TTT
  fair TTT
  fair HTT
  fair HTT
  fair THT
  fair THT
  fair HHT *
  fair HHT *
  fair THT
  fair THT
  fair HHT *
  fair HHT *
  fair TTT
  fair TTT
  fair HTH
  fair HTH
  fair TTH
  fair TTH
  fair HTH
  fair HTH
  fair THH
  fair THH
unfair HHH
unfair HHH
unfair HHH
unfair THH
unfair HHH
unfair HHH
unfair HHH
unfair THH
unfair HHH
unfair HHH
unfair HTH
unfair TTH
unfair HTH
unfair HTH
unfair HHH
unfair THH
unfair HHH
unfair HHH
unfair HHH
unfair THH
unfair HHH
unfair HHH
unfair HHH
unfair THH
unfair HHH
unfair HHH
unfair HTH
unfair TTH
unfair HTH
unfair HTH
unfair HHH
unfair THH
unfair HHH
unfair HHH
unfair HHH
unfair THH
unfair HHH
unfair HHH
unfair HHH
unfair THH
unfair HHT *
unfair HHT *
unfair HTT
unfair TTT
unfair HTT
unfair HTT
unfair HHT * 
unfair THT
unfair HHT *
unfair HHT *
unfair HHT *
unfair THT
unfair HHT *
unfair HHT *
unfair HHT *
unfair THT
unfair HHH
unfair HHH
unfair HTH
unfair TTH
unfair HTH
unfair HTH
unfair HHH
unfair THH

  Posted by Charlie on 2016-03-18 11:10:23
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information