An Urn Has 3 Red Balls 4 Blue Balls and 5 Green Balls Alice
Math Expert
Joined: 02 Sep 2009
Posts: 86397
A bag contains blue and red balls only. [#permalink] 
07 Oct 2020, 23:15
00:00
Question Stats:
64% (01:44) correct 36% (01:59) wrong based on 61 sessions
Hide Show timer Statistics
A bag contains blue and red balls only.
If one ball is drawn, the probability of selecting a blue ball is 1/2.
If two balls are drawn randomly without replacement, the probability of selecting a blue and then a red ball is 5/18.
Two balls are drawn randomly without replacement, what is the probability of drawing a red ball, given that the first ball drawn was blue?
(A) 2/9
(B) 5/18
(C) 4/9
(D) 1/2
(E) 5/9
Project PS Butler
Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS
_________________
Math Expert
Joined: 02 Aug 2009
Posts: 10472
A bag contains blue and red balls only. [#permalink] 08 Oct 2020, 00:28
A bag contains blue and red balls only. .....Let it be b and r
If one ball is drawn, the probability of selecting a blue ball is 1/2.......
So, \(\frac{b}{b+r}=\frac{1}{2}\) or \(b=r\)
If two balls are drawn randomly without replacement, the probability of selecting a blue and then a red ball is 5/18.......
So, \(\frac{b}{b+r}*\frac{r}{b+r-1}=\frac{1}{2}*\frac{r}{2r-1}=\frac{5}{18}.........\)
\(\frac{r}{2r-1}=\frac{5}{18}*2=\frac{5}{9}........9r=5(2r-1)=10r-5.....r=5=b\)
Two balls are drawn randomly without replacement, what is the probability of drawing a red ball, given that the first ball drawn was blue?
We are looking for probability of picking one red ball from a pool of 5 red and 4 blue balls => \(\frac{5}{5+4}=\frac{5}{9}\)
E
_________________
Director
Joined: 08 Aug 2017
Posts: 739
Re: A bag contains blue and red balls only. [#permalink] 08 Oct 2020, 01:22
Only two type- blue & red- balls are there.
P(blue) = 1/2 means there are equal red and blue balls.
So probability of withdrawal of two balls without replacement- first blue and then second= 1/2*{(x)/2x-1} = 5/18
Therefore, x= 5
Now probability of withdrawal of red balls at second when first withdrawn ball is blue. = 5/9
E is answer.
Senior Manager
Joined: 27 Feb 2014
Posts: 481
Location: India
Concentration: General Management, International Business
GMAT 1: 570 Q49 V20 
GPA: 3.97
WE:Engineering (Education)
A bag contains blue and red balls only. [#permalink] 08 Oct 2020, 03:27
Quote:
A bag contains blue and red balls only.
If one ball is drawn, the probability of selecting a blue ball is 1/2.
If two balls are drawn randomly without replacement, the probability of selecting a blue and then a red ball is 5/18.
Two balls are drawn randomly without replacement, what is the probability of drawing a red ball, given that the first ball drawn was blue?
Step 1: Understanding the question
When probability of selecting a blue ball is 1/2 = 50%, probability of selecting a red ball is also 1/2 = 50%, therefore number of blue and red balls are equal.
Let number of blue balls = number of red balls = x; total number of balls = 2x
probability of selecting a blue = \(\frac{x}{2x}\) and then a red ball = \(\frac{x}{(2x-1) }\)
probability of selecting a blue and then a red ball = \(\frac{x}{2x}\) * \(\frac{x}{(2x-1)}\) = 5/18
Simplifying, x = 5
Number of blue balls = number of red balls = 5; Total number of balls = 10
Step 2: Calculation
probability of drawing a red ball, given that the first ball drawn was blue
When first blue ball is drawn, total number of balls left = 9
Probability of drawing a red ball out of 9 balls = 5/9
E is correct
_________________
GMAT Number Properties 101 Solved Questions: https://amzn.to/39zSKVM
Current Student
Joined: 29 Dec 2019
Posts: 77
Re: A bag contains blue and red balls only. [#permalink] 08 Oct 2020, 05:02
Two statements
If two balls are drawn randomly without replacement, the probability of selecting a blue and then a red ball is 5/18.
First select BLUE and then RED
Two balls are drawn randomly without replacement, what is the probability of drawing a red ball, given that the first ball drawn was blue?
First select BLUE and then RED
Both imply the same meaning? I am confused.
CR Forum Moderator
Joined: 14 Mar 2018
Posts: 615
Re: A bag contains blue and red balls only. [#permalink] 08 Oct 2020, 05:22
IMO E
We've been given that :
P(B)=1/2 which means that the number of blue and red balls are equal.
Now, probability of selecting a blue and then a red ball is 5/18 (if two balls are drawn without replacement.
1/2* (x/2x-1)= 5/18 , which will give you the number of red balls = 5.
Hence, P(red ball)= 5/9
Math Expert
Joined: 02 Aug 2009
Posts: 10472
A bag contains blue and red balls only. [#permalink] 08 Oct 2020, 06:34
Target4bschool wrote:
Two statements
If two balls are drawn randomly without replacement, the probability of selecting a blue and then a red ball is 5/18.
First select BLUE and then RED
Two balls are drawn randomly without replacement, what is the probability of drawing a red ball, given that the first ball drawn was blue?
First select BLUE and then RED
Both imply the same meaning? I am confused.
The second case
......Here blue is already chosen. Now you have to choose Red. So, it basically means choosing RED from total number -1....-1 is the first pick that is already done
_________________
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 11852
GPA: 3.82
Re: A bag contains blue and red balls only. [#permalink] 08 Oct 2020, 07:23
P(B) = \(\frac{1}{2}\)
Two balls are drawn [without replacement]: P(a blue and then a red ball is \(\frac{5}{18}\)) - This means it is an independent even and hence P(B ∩ R) = P(B) * P(R)
Probability of drawing a red ball, given that the first ball drawn was blue - Conditional Probability
=> P(\(\frac{R}{B}\)) = \(\frac{[P(B ∩ R)] }{ P(B)}\)
=> P(\(\frac{R}{B}\)) = \(\frac{\frac{5}{18}}{0.5}\)
=> P(\(\frac{R}{B}\)) = \(\frac{5}{9}\)
Answer E
_________________
Re: A bag contains blue and red balls only. [#permalink]
08 Oct 2020, 07:23
Moderators:
Senior SC Moderator
5457 posts
Senior Moderator - Masters Forum
2926 posts
gonsalezwitivelittly38.blogspot.com
Source: https://gmatclub.com/forum/a-bag-contains-blue-and-red-balls-only-336061.html
0 Response to "An Urn Has 3 Red Balls 4 Blue Balls and 5 Green Balls Alice"
Post a Comment