My Math Forum  

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

Advanced Statistics Advanced Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
July 10th, 2012, 03:20 PM   #1
Senior Member
 
Chikis's Avatar
 
Joined: Jan 2012

Posts: 724
Thanks: 7

Probability That They Are One Red, One White And One Blue Ba

Three balls are drawn one after the other with replacement, from a bag containing 5 red, 9 white and 4 blue identical balls. What is the probability that they are one red, one white and one blue balls?
Please I need working and explaination.
Chikis is offline  
 
July 10th, 2012, 07:44 PM   #2
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,205
Thanks: 512

Math Focus: Calculus/ODEs
Re: Probability That They Are One Red, One White And One Blu

The probability of getting a red ball is:



The probability of getting a white ball is:



The probability of getting a blue ball is:



Hence, the probability of getting all 3 is:



Now we must consider that there are 3! = 6 ways to order the 3 balls, hence the final probability is:

MarkFL is offline  
July 10th, 2012, 10:27 PM   #3
Senior Member
 
Chikis's Avatar
 
Joined: Jan 2012

Posts: 724
Thanks: 7

Re: Probability That They Are One Red, One White And One Blu

@MarkFL
The question demands that I evaluate the probability that they are one red, one white and one blue balls in the three draws held.
They did not give the order which the draws will follow, I therefore assume it could be in order.

My working:
Total number of balls = 18
P(r) = 5/18
P(w) = 9/18 = 1/2
P(b) = 4/18 = 2/9
The probability that they are one red, one white and one blue balls = P(1st-r,2nd-w,3rd-b) Or P(1st-w,2nd-b,3rd-r) Or P(1st-b, 2nd-r,3rd-w)
(5/18*1/2*2/9) + (1/2*2/9*5/1 + (2/9*5/18*1/2)
= 10 + 10 + 10/324
= 30/324
= 5/54
But the answer I got did not match with the answer they provided for the question. Is my working wrong or did I not follow the right principle?
Lets compare our working: in your own, they are six orders but in mine they are three orders instead of six.

Your own ------> 60/324 = 5/27

My own ------> 30/324 = 5/54

What made you believe that they are six others instead of three? Or how do I know the number of orders in probability like this?
Chikis is offline  
July 10th, 2012, 10:51 PM   #4
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,205
Thanks: 512

Math Focus: Calculus/ODEs
Re: Probability That They Are One Red, One White And One Blu

We have 3 choices for the first draw, 2 for the second and 1 for the last, giving 3! = 3򈭽 = 6 six permutations:

RWB
RBW
WRB
WBR
BRW
BWR
MarkFL is offline  
July 11th, 2012, 12:50 AM   #5
Senior Member
 
Chikis's Avatar
 
Joined: Jan 2012

Posts: 724
Thanks: 7

Re: Probability That They Are One Red, One White And One Blu

Remeber, the three balls are drawn one after the other with replacement.
Chikis is offline  
July 11th, 2012, 12:54 AM   #6
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,205
Thanks: 512

Math Focus: Calculus/ODEs
Re: Probability That They Are One Red, One White And One Blu

Yes, that doesn't change the number of permutations of the possible ordering.
MarkFL is offline  
July 11th, 2012, 01:21 AM   #7
Senior Member
 
Chikis's Avatar
 
Joined: Jan 2012

Posts: 724
Thanks: 7

Re: Probability That They Are One Red, One White And One Blu

If that be the case, that implies that even if two balls of colours say white and yellow are drawn one after the other, wether with or without replacement, in finding the of probability of getting one white and one yellow will be held in this order
-------->
(two choices for the first draw) + (one choice for the second draw being the last) draw.

i.e 2:1, suming up the total draws to 3.
Isn't it?
Chikis is offline  
July 11th, 2012, 01:25 AM   #8
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,205
Thanks: 512

Math Focus: Calculus/ODEs
Re: Probability That They Are One Red, One White And One Blu

No, we don't add, we multiply 21 = 2:

WY
YW
MarkFL is offline  
July 11th, 2012, 01:55 AM   #9
Senior Member
 
Chikis's Avatar
 
Joined: Jan 2012

Posts: 724
Thanks: 7

Re: Probability That They Are One Red, One White And One Blu

I think it is important at this juncture that I inform you that your system of working is quite different from the working and answers provided by the people who set the question.
Here is the list of possible answers based on how you do the workings. A. 5/102 B. 5/136 C. 5/162 D. 5/204 E. 5/243.
It is unforturnate to note that your working did not fall into any of these answers.
Here is their own working:
Total number of balls = 18
P(1R, 1W, 1B) = 5/18 * 1/2 * 2/9 = 5/162 = option C.
What do you have say about it?
Chikis is offline  
July 11th, 2012, 02:09 AM   #10
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,205
Thanks: 512

Math Focus: Calculus/ODEs
Re: Probability That They Are One Red, One White And One Blu

That would be the correct answer if a particular order is required for the 3 colors.

For example, if it is required to draw a red ball first, then a white ball second, then lastly a blue ball, then the probability 5/162.

This was not made clear in the original statement of the problem. No order was implied, at least by my interpretation of the problem.
MarkFL is offline  
Reply

  My Math Forum > College Math Forum > Advanced Statistics

Tags
blue, probability, red, white



Search tags for this page
There are 4 red balls, 6 white balls, and 3 blue balls in a bag. If one ball is drawn from the bag at random, what is the probability that it is not white?
,

White = 5, Red = 8 and Blue = 1

,

we have 8 red balla 3 white and 9 blue balss if 3 drawn at random find the probability all the balls are of diffrent colours

,

3 red, 4 white and 5 blue. 3 balls are drawn from box one after without replacemen. find probability that 3 are blue.

,

A bag contains 7 green, white and 3 red balls.If 3 balls are drawn at random determine the probability that (a) all 3 are white (b) at least 1 is green

,

a bag contain 6 white and 9 black balls.four balls are drawn at a time.find probability for first draw to give 4 white balls and second draw to give 4 black balls

,

if you are asked to draw a white ball from a bag of blue balls, the probability that a white ball will be drawn is 0

,

a bag contains 5 white 3 red and 4 black balls two balls r drawn one after the other with replacement and without replacement

,

there are 3 white 4 black and 5 red balls.if 3 balls are drawn in succession without replacement.find the probability that all are of different colours.

,

A bag contains 8 blue balls and 5 black balls. 2 successive draws of 3 balls are made without replacement. Find the probability that the first drawing will give 3 black balls and the second 3 blue balls.

,

probability of getting all white balls from a bag containiw qhite red black balla

,

a bag contains 5 red and 4 blue balla,2balls are drawsn from the bag one after the other with replacement,find the probability that the balls drawn are of the same color

,

a bag contains 2 red,3 white,4 yellow balls.if the 3 balls are drawn in successionwith replacement,what is the probability that the first ball is red,the second is white & third is yellow

,

a bag contains 7 green, 4 white and 5 red balls. If four balls are drawn one by one without replacement, what is the probability that one is red?

,

a bag contains 7 yellow balls and 5 red balls. one ball is taken from the bag at random and not replaced. a second ball is taken from the bag . determine the probability of both the balls are different colors

Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
A box contains 3 white, 8 red, 9 blue r-soy Algebra 3 October 12th, 2013 02:54 PM
The Probability That Exactly One Of The Four Balls Is White Chikis Advanced Statistics 11 October 9th, 2012 12:41 PM
The probability that: two are white and one is blue. Chikis Advanced Statistics 13 August 21st, 2012 02:50 PM
5 Blue, 10 Red, 15 green balls. Odds I will draw 5 blue 1st? mimath123 Advanced Statistics 1 February 21st, 2010 04:24 PM
white noise/iid jlt1209 Advanced Statistics 0 February 2nd, 2009 07:00 PM





Copyright © 2018 My Math Forum. All rights reserved.