My Math Forum  

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

Probability and Statistics Basic Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
October 18th, 2013, 11:02 PM   #1
Newbie
 
Joined: Oct 2013

Posts: 10
Thanks: 0

Basic probability

An urn contains 7 red marbles labeled {1,2,3,4,5,6,7} and 5 green marbles labeled {1,2,3,4,5}. Four
marbles are pulled out at once (i.e. with no particular order). What is the probability that

(a) all four marbles are red?


(b) more of the marbles are green than red?


(c) both red and green marbles are present?


(d) two of the marbles chosen are both labeled "5"?
xsgx is offline  
 
October 19th, 2013, 04:09 PM   #2
Newbie
 
Joined: Oct 2013

Posts: 10
Thanks: 0

Re: Basic probability

bump
xsgx is offline  
October 19th, 2013, 05:22 PM   #3
Math Team
 
Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

Re: Basic probability

Hello, xsgx!

Quote:
An urn contains 7 red marbles labeled {1,2,3,4,5,6,7} and 5 green marbles labeled {1,2,3,4,5}.
Four marbles are pulled out at once (i.e. with no particular order).




Quote:
What is the probability that:
(a) all four marbles are red?




Quote:
(b) more of the marbles are green than red?








Quote:
(c) both red and green marbles are present?










Quote:
(d) two of the marbles chosen are both labeled "5"?






soroban is offline  
October 19th, 2013, 06:03 PM   #4
Newbie
 
Joined: Oct 2013

Posts: 10
Thanks: 0

Re: Basic probability

Wow, thank you! Just what I needed, a step by step explanation.
xsgx is offline  
October 21st, 2013, 05:18 AM   #5
Newbie
 
Joined: Oct 2013

Posts: 9
Thanks: 0

Re: Basic probability

Very neat solution. My mind did not think as laterally as you did.
By thinking "aloud", I could do (a), the first part of (b) and (c) with some luck.
For (a), I did 7/12 x 6/11 x 5/10 x 4/9 = =7/99
For straightforward 4 greens, I got 1/99; I was then faced with doing all the combinations of greens and red.
Well done.
nubian123 is offline  
October 21st, 2013, 09:31 PM   #6
jks
Senior Member
 
jks's Avatar
 
Joined: Jul 2012
From: DFW Area

Posts: 635
Thanks: 96

Math Focus: Electrical Engineering Applications
Re: Basic probability

[color=#0000BF]nubian123[/color],

Using your method, the probabilities of the various combinations of greens and reds are not too hard to calculate:







The factorial expressions multiplied at the end are the number of permutations in the order that the marbles may be picked. For example, with 1 green and 3 red; GRRR, RGRR, RRGR, RRRG gives 4. For 2 green, 2 red; RRGG, RGRG, RGGR, GRRG, GRGR, GGRR gives 6.

Notice that all probabilities add to 1 as they should:



d) is worked as:

jks is offline  
Reply

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

Tags
basic, probability



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Basic probability question daigo Probability and Statistics 5 February 5th, 2012 12:14 PM
Basic Probability jskrzy Probability and Statistics 5 October 17th, 2011 12:29 PM
Basic Probability questions Turloughmack Probability and Statistics 1 January 21st, 2011 08:43 AM
Basic Probability help downthesun01 Algebra 1 October 7th, 2009 02:49 AM
Basic probability jackal_00 Advanced Statistics 6 April 3rd, 2008 07:05 PM





Copyright © 2019 My Math Forum. All rights reserved.