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by crackgmat007 » Tue Oct 13, 2009 7:06 am
A basket contains 3 white and 5 blue balls. Mary will extract one ball at random and keep it. If, after that, John will extract one ball at random, what is the probability that John will extract a blue ball?
Last edited by crackgmat007 on Tue Oct 13, 2009 7:47 am, edited 1 time in total.
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Re: Blue balls

by aa2kash » Tue Oct 13, 2009 7:24 am
crackgmat007 wrote:A basket contains 3 white and 5 blue balls. Mary will extract one ball at random and keep it. If, after that, John will extract one ball at random, what is the probability that John will extract a blue ball?
My Answer is 35/48.
took 2 cases. 1 mary draws a blue ball and in 2nd if mary draws a white.

Whats the OA
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by crackgmat007 » Tue Oct 13, 2009 7:26 am
OA - [spoiler]5/8[/spoiler]
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by mp2437 » Tue Oct 13, 2009 7:44 am
Title of this thread may be a bit scary for some. :lol:
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by aa2kash » Tue Oct 13, 2009 7:45 am
MY mistake :)
I did 8*7= 48
yes the answer is 35/56 = 5/8

Explaination : 3W and 5B balls are there.
case1 mary draws a white ball and then john draws a blue ball : p=3/8 * 5/7 =15/56
note when a white ball is withdrawn there are total 7 balls remaining.
case2 mary draws a blue ball and then john draws a blue ball : p=5/8 * 4/7=20/56
so final prob is 15/56+20/56 =35/56=5/8
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by sumitha_ambati » Tue Oct 13, 2009 7:57 am
we hav 2 cases here
1. mary picks a white ball = 3/8 * 5/7
2. mary picks a blue ball = 5/8 * 4/7

= 15/56 + 20/56
= 35/56 = 5/8
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by 2010gmat » Tue Oct 13, 2009 10:13 am
if mary picks white ball

3/8)*(5/7) --1.)

if mary picks blue ball

(5/8)*(4/7) --2.)

--> probability of John drawing a blue ball = 1.) + 2.)

= 5/8
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by sanjana » Wed Oct 14, 2009 4:30 am
I dont think Any calculation is required here.

It doesnt matter what Mary picks because she is replacing it!
So for John its as good as picking from the entire set of 3w and 5b
P(picking a blue ball) = 5c1/8c1 = 5/8
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by 2010gmat » Wed Oct 14, 2009 4:34 am
Mary is drawing one ball and keeping it...the question does not say keeping it back
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by Brent@GMATPrepNow » Fri Jan 10, 2020 5:46 am
crackgmat007 wrote:A basket contains 3 white and 5 blue balls. Mary will extract one ball at random and keep it. If, after that, John will extract one ball at random, what is the probability that John will extract a blue ball?
This question reminds me of my childhood, when my friends and I would sometimes "draw straws" to randomly select one person to do something (often either work, like getting wood for the fire, or dumb, like eating something that shouldn't be eaten).

So, someone would hold up n pieces of grass (for n guys), and one of those pieces was very short. The person who selected the shortest piece was the one who had to perform the task.

There was always one guy who wanted to choose his piece last. His reasoning was that his chances of drawing the shortest piece were minimized since every person before him had a chance of drawing the short piece before it got to his turn.

The truth of the matter is that each of the n guys had a 1/n chance of selecting the shortest piece, regardless of the order in which they selected.

The same applies to the original question here. 5 of the 8 balls are blue, so P(John selects a blue ball) = 5/8

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Brent
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by Brent@GMATPrepNow » Fri Jan 10, 2020 5:46 am
crackgmat007 wrote:A basket contains 3 white and 5 blue balls. Mary will extract one ball at random and keep it. If, after that, John will extract one ball at random, what is the probability that John will extract a blue ball?
Let's solve this question a different way.

P(John gets blue ball) = P(Mary gets white ball and John gets blue ball OR Mary gets blue ball and John gets blue ball
= P(Mary gets white ball and John gets blue ball) + P(Mary gets blue ball and John gets blue ball)
= (3/8 x 5/7) + (5/8 x 4/7)
= 15/56 + 20/56
= 35/56
= 5/8

Answer: still D :-)

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