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# A bag contains 3 red and 2 black ball. Another bag contains 4 red and

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Director
Status: Everyone is a leader. Just stop listening to others.
Joined: 22 Mar 2013
Posts: 693
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)
A bag contains 3 red and 2 black ball. Another bag contains 4 red and  [#permalink]

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07 Aug 2013, 04:41
4
32
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Difficulty:

95% (hard)

Question Stats:

14% (02:03) correct 86% (02:13) wrong based on 271 sessions

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A bag contains 3 red and 2 black ball. Another bag contains 4 red and 5 black balls. A ball is drawn from the first bag and is placed in the second. A ball is then drawn from the second. What is the probability that this draw of red ball is due to the drawing of red ball from the first bag ?

A. 3/5
B. 2/5
C. 4/25
D. 3/10
E. 15/23
Senior Manager
Joined: 20 Aug 2015
Posts: 382
Location: India
GMAT 1: 760 Q50 V44
A bag contains 3 red and 2 black ball. Another bag contains 4 red and  [#permalink]

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23 Nov 2015, 03:21
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1
3
PiyushK wrote:
A bag contains 3 red and 2 black ball. Another bag contains 4 red and 5 black balls. A ball is drawn from the first bag and is placed in the second. A ball is then drawn from the second. What is the probability that this draw of red ball is due to the drawing of red ball from the first bag ?

A. 3/5
B. 2/5
C. 4/25
D. 3/10
E. 15/23

Given:
Bag 1: 3 Red, 2 Black
Bag 2: 4 Red, 5 Black

1st transaction:
A ball is moved from bag 1 and shifted to bag 2
P(R) = $$\frac{3}{5}$$ and P(B) = $$\frac{2}{5}$$

2nd Transaction:
A ball is picked from the Bag 2.

Required: Probability that this draw of red ball is due to the drawing of red ball from the first bag

Case 1: Black ball was picked from Bag 1 and then a Red is picked from Bag 2
P(R) = $$\frac{2}{5}*\frac{4}{10} = \frac{8}{50}$$
Case 2: Red ball was picked from Bag 1 and then a Red is picked from Bag 2
P(R) =$$\frac{3}{5}*\frac{5}{10}= \frac{15}{50}$$

We need the probability of occurrence off Case 2:
Hence P(Case 2) =$$\frac{15}{50} / (\frac{8}{50} + \frac{15}{50}) = \frac{15}{23}$$
Option E
Intern
Joined: 05 Apr 2010
Posts: 11
Re: A bag contains 3 red and 2 black ball. Another bag contains 4 red and  [#permalink]

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07 Aug 2013, 08:05
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Probability of getting red ball from bag1 and then red from bag 2 = 3/5*5/10 = 15/50
Probability of getting black ball from bag1 and then red from bag 2 = 2/5*4/10 = 8/50

Now comes the condition, hence apply conditional probability:
P(Red)/ P(Red + Black)

(15/50)/(15/50+8/50) = 15/50 /23/50 = 15/23.
IMO E
##### General Discussion
Manager
Joined: 14 Aug 2005
Posts: 55
Re: A bag contains 3 red and 2 black ball. Another bag contains 4 red and  [#permalink]

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07 Aug 2013, 06:35
1
PiyushK wrote:
A bag contains 3 red and 2 black ball. Another bag contains 4 red and 5 black balls. A ball is drawn from the first bag and is placed in the second. A ball is then drawn from the second. What is the probability that this draw of red ball is due to the drawing of red ball from the first bag ?

A. 3/5
B. 2/5
C. 4/25
D. 3/10
E. 15/23

I got the answer as D

3/5*5/10 = 3/10

Director
Status: Everyone is a leader. Just stop listening to others.
Joined: 22 Mar 2013
Posts: 693
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)
Re: A bag contains 3 red and 2 black ball. Another bag contains 4 red and  [#permalink]

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07 Aug 2013, 07:24
1
surya167 wrote:
PiyushK wrote:

There are two possible cases, out of those two we have to calculate the possibility of case 1.

case 1. one red ball was transferred to second bag, and then red ball is drawn from bag2.
or
case 2. one black ball was transferred to second bag, and then red ball is drawn from bag2.

Both cases are possible but we have to find out occurrence of case 1 out of these two cases.

I think this much hint is sufficient bcz solution is just single step away.
Try, else i will post my solution.
Manager
Joined: 06 Jul 2013
Posts: 80
GMAT 1: 620 Q48 V28
GMAT 2: 700 Q50 V33
Re: A bag contains 3 red and 2 black ball. Another bag contains 4 red and  [#permalink]

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07 Aug 2013, 08:02
i got the D but after the hint it got E.

.3/.3+.16 = 15/23

Thanks
Manager
Joined: 14 Aug 2005
Posts: 55
Re: A bag contains 3 red and 2 black ball. Another bag contains 4 red and  [#permalink]

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07 Aug 2013, 08:34
coolpintu wrote:
Probability of getting red ball from bag1 and then red from bag 2 = 3/5*5/10 = 15/50
Probability of getting black ball from bag1 and then red from bag 2 = 2/5*4/10 = 8/50

Now comes the condition, hence apply conditional probability:
P(Red)/ P(Red + Black)

(15/50)/(15/50+8/50) = 15/50 /23/50 = 15/23.
IMO E

Thanks, now i understand. I was missing the point of conditional probability totally!
Senior Manager
Joined: 10 Jul 2013
Posts: 280
Re: A bag contains 3 red and 2 black ball. Another bag contains 4 red and  [#permalink]

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07 Aug 2013, 08:49
surya167 wrote:
coolpintu wrote:
Probability of getting red ball from bag1 and then red from bag 2 = 3/5*5/10 = 15/50
Probability of getting black ball from bag1 and then red from bag 2 = 2/5*4/10 = 8/50

Now comes the condition, hence apply conditional probability:
P(Red)/ P(Red + Black)

(15/50)/(15/50+8/50) = 15/50 /23/50 = 15/23.
IMO E

Thanks, now i understand. I was missing the point of conditional probability totally!

very well explained......coolpintu
Intern
Joined: 27 Oct 2015
Posts: 6
A bag contains 3 red and 2 black ball. Another bag contains 4 red and  [#permalink]

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22 Nov 2015, 10:23
I did it like this:-
There are three cases,when we fix that the ball drawn from second box is red
1)red ball drawn from first box and it is picked from second - 3/5*1/10
2)red ball drawn from first box and other red ball is picked - 3/5*4/10
3)black ball is drawn from first box and red ball is picked - 2/5*4/10

First is the favourable option, so i did (3/5*1/10)/(3/5*4/10 + 2/5*4/10) =3/23 which is none of the option.

Please anyone let me know what i have missed here..

Ohh got it ..i think i mis-interpreted the question as i thought that the red ball drawn from the second box should be the one that is drawn from first.

So favourable option should be 1 and 2 both which will give me 15/23..

Anyone got that misunderstanding??
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Posts: 9142
Location: United States (CA)
Re: A bag contains 3 red and 2 black ball. Another bag contains 4 red and  [#permalink]

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01 Mar 2018, 18:30
PiyushK wrote:
A bag contains 3 red and 2 black ball. Another bag contains 4 red and 5 black balls. A ball is drawn from the first bag and is placed in the second. A ball is then drawn from the second. What is the probability that this draw of red ball is due to the drawing of red ball from the first bag ?

A. 3/5
B. 2/5
C. 4/25
D. 3/10
E. 15/23

The ball transferred from the first bag to the second could be a black ball or a red ball. Therefore, we have two scenarios:

1) A red ball is drawn from the 2nd bag after a black ball is drawn from 1st bag and transferred to the 2nd bag.

2) A red ball is drawn from the 2nd bag after a red ball is drawn from 1st bag and transferred to the 2nd bag.

Let’s find the probability of each scenario:

1) P(1st = black, 2nd = red) = 2/5 x 4/10 = 8/50

2) P(1st = red, 2nd = red) = 3/5 x 5/10 = 15/50

Thus the probability of drawing a red ball from the 2nd bag is 8/50 + 15/50 = 23/50, and the probability that it is due to a red ball having been drawn from the 1st bag is:

(15/50)/(23/50) = 15/23

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Re: A bag contains 3 red and 2 black ball. Another bag contains 4 red and  [#permalink]

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08 May 2019, 09:53
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Re: A bag contains 3 red and 2 black ball. Another bag contains 4 red and   [#permalink] 08 May 2019, 09:53
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