
Probability and Statistics Basic Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
January 31st, 2010, 12:38 AM  #1 
Senior Member Joined: Jan 2010 Posts: 205 Thanks: 0  Probability of having one of two unknown bags Bag #1 900 red eggs 100 blue eggs Bag #2 100 red eggs 900 blue eggs You are given one of these two bags (50/50 chance) randomly. You perform a set of trials where you take out one egg randomly from your bag, note the color, then put it back in, and repeat. You drew 8 red eggs and 2 blue eggs from your bag during this trial. What is the probabilty (%) that you have Bag #1? I thought it was 50% because you could have drawn 8 red and 2 blue from bag #2 as well, since drawing eggs and putting them back does not change the bag's contents... 
January 31st, 2010, 10:33 AM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 406  Re: Probability of having one of two unknown bags Hello, daigo! I solved this at another site . . . but here it is again. Quote:
This is Conditional Probability. [color=beige] .[/color][color=blue][1][/color] [color=beige]. . [/color] [color=beige]. . [/color] [color=beige]. . [/color][color=beige] .[/color][color=blue][2][/color] [color=beige]. . [/color] [color=beige]. . [/color] [color=beige]. . [/color][color=beige] .[/color][color=red](A)[/color] [color=beige] .[/color][color=blue][3][/color] Substitute [color=blue][2][/color] and [color=blue][3][/color] into [color=blue][1][/color]: [color=beige]. . [/color] ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ This result make sense when we consider [color=red](A)[/color]. [color=beige]. . [/color] If we have Bag 2, it is virtually impossible to draw 8 Reds and 2 Blues. Thereofore, they must have come from Bag 1.  
January 31st, 2010, 12:11 PM  #3 
Senior Member Joined: Jan 2010 Posts: 205 Thanks: 0  Re: Probability of having one of two unknown bags
Thanks. I was shown another method where I do 100  ([1^8 * 100] / [9^8]) but I did not understand why that was the answer. Your solution clarified it better.


Tags 
bags, probability, unknown 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
women and bags  shunya  Algebra  5  February 27th, 2014 11:07 PM 
x^e mod P where x is unknown  zxcvbnm123  Number Theory  1  February 19th, 2014 02:26 AM 
Conceptual real world math problem. Balls in Bags  dragonaut  Algebra  0  March 27th, 2013 12:46 PM 
Bags and Balls  drunkd  Algebra  8  July 31st, 2012 04:32 AM 
Unknown Topic  benathan  Calculus  7  September 20th, 2007 05:48 PM 