My Math Forum  

Go Back   My Math Forum > High School Math Forum > Probability and Statistics

Probability and Statistics Basic Probability and Statistics Math Forum

Thanks Tree1Thanks
  • 1 Post By romsek
LinkBack Thread Tools Display Modes
April 6th, 2017, 03:48 PM   #1
Senior Member
Joined: Oct 2013
From: New York, USA

Posts: 590
Thanks: 81

Probability Question With Different People Knowing Different Information

People A, B, C, and D make drawings A, B, C, D, respectively. Each person makes one drawing and knows that each person made one drawing. The drawings are collected, and everybody guesses who made each drawing. All four people guess without knowing how the other people guessed. Everybody knows their own drawing and randomly guesses for the other three.

1. Since each person has a 1/3 chance of guessing each of the three drawing he didn't make, does that mean the average number of correct guesses per person is 1 (2 including the person knowing their own drawing)? Is it more complicated than that?

2. There are 3! = 6 permutations of 3 drawings, so I'm assuming each person has a 1/6 chance at correctly guessing all 3 drawings he didn't make. How well each person guesses is independent of how well the other people guess, so are these correct?

P(everybody guesses everything correct) = (1/6)^4 = 1/1,296
P(at least one person guesses everything correct) = 1 (5/6)^4 = 671/1,296 = about 51.8%
EvanJ is offline  
April 6th, 2017, 07:49 PM   #2
Senior Member
romsek's Avatar
Joined: Sep 2015
From: USA

Posts: 1,785
Thanks: 920

1) It's a bit more complicated than that.

Each person is faced with matching 3 painters to 3 paintings. If you look at how correct guesses are distributed you get

$P[\text{k correct guesses}] =
\dfrac 1 3 &k=0 \\
\dfrac 1 2 &k=1 \\
0 &k=2 \\
\dfrac 1 6 &k=3

The expected value does happen to equal 1.

If each person painted 3 paintings, and out of those 3 1 was selected, and you had to select the painter that would be the situation you described. Here we "select w/o replacement". We'll never select the same painter twice.

Looking at (2)

You have $P[\text{everyone guesses all correctly}]=(1/6)^4$ correct

You have the second one correct too though you left out a minus sign.

well done
Thanks from EvanJ
romsek is offline  

  My Math Forum > High School Math Forum > Probability and Statistics

information, knowing, people, probability, question

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Probability that k people choose the same set of n numbers m3g4n Probability and Statistics 7 October 28th, 2016 10:32 AM
Probability of two people meeting hdpeterson75 Applied Math 0 November 26th, 2015 05:49 PM
Probability of the Truthfulness of a Group of People lavitz Advanced Statistics 1 May 22nd, 2013 02:10 PM
Information content and probability - opinion needed baxy7 Advanced Statistics 7 August 24th, 2010 07:06 AM
probability of getting a specific cardgroup with 9 people durexlw Algebra 0 April 5th, 2009 04:54 AM

Copyright © 2018 My Math Forum. All rights reserved.