My Math Forum  

Go Back   My Math Forum > College Math Forum > Advanced Statistics

Advanced Statistics Advanced Probability and Statistics Math Forum

LinkBack Thread Tools Display Modes
March 3rd, 2014, 11:05 AM   #1
Joined: Mar 2014

Posts: 1
Thanks: 0

Bayes Theory (Is this a trick question)

A conditional probability problem that I can't figure out:

(PART 1) Tom is trying to figure out the probability that his memory of a ride in a fighter jet when he was a toddler is real or if it is just a product of his imagination. He grew up near an air force base -- the odds of a child in that area taking a ride on a fighter jet are 1/1000. Because he has no bias towards whether the event happened or not -- he is 50 percent sure it did, 50 percent sure it did not -- per Bayes's theory, there is a 1/1000 chance it did, the prior odds.

(Is the assumption above true (y/n): Y

(PART 2) If it is true, please answer the following: Of those that correctly recalled riding on the fighter jet (they actually did), 1/2 remembered spontaneously and 1/2 were actively thinking about their childhood. Of those that did not ride on the jet and merely imagined it, 1/100 remembered spontaneously, 99/100 were actively thinking about their childhood. If we were 100 percent sure that Tom remembered while actively thinking about his childhood, how does this affect the probability that he actually rode on the fighter jet? What we were 75 percent certain? And 50 percent? And, finally, 25 percent? Is it impossible to calculate?

To start, we can conclude that of 1000 children the following is true:

a. Spontaneous Recall (1/2 * 1) = 1/2 child c. Spontaneous Recall (1/100 * 999) = 9.99 children
b. Active Recall (1/2 * 1) = 1/2 child d. Active Recall (99/100 * 999) = 989.01 children

Regarding 100 percent -- this seems straight-forward. If Tom is 100 percent sure he remembered while actively thinking about his childhood, then the odds of him riding on the jet would be expressed as b / d.

And the probability would be unchanged for 50 percent -- this assumes we have no idea if the memory was spontaneously recalled or not, so the prior odds would remain.

Regarding 25 and 75 percent: the only way I can think of solving is by averaging the values we got for 100 and 50 percent. What would be the formulaic way to solve? I thought I was pretty proficient as Bayes theory, I just can't wrap my head around this one. I don't know which prior probability I should start with.
redsox123 is offline  

  My Math Forum > College Math Forum > Advanced Statistics

bayes, question, theory, trick

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Is this a trick question? Converting Shamieh Algebra 3 May 29th, 2013 06:39 AM
trick question mathkid Algebra 3 February 25th, 2013 03:51 AM
Is this Trick Question?? mathkid Calculus 1 September 22nd, 2012 11:42 AM
bayes theorem question tnutty Advanced Statistics 2 March 17th, 2011 01:52 AM
Bayes's Theorem Question Answer Check Gordie83 Advanced Statistics 2 January 6th, 2009 06:15 AM

Copyright © 2019 My Math Forum. All rights reserved.