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# gmatclub test question : mary and john

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Senior Manager
Joined: 06 Jul 2007
Posts: 268
gmatclub test question : mary and john [#permalink]

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18 Mar 2009, 13:10
The basket contains 3 white and 5 blue balls. Mary will extract one ball at random and keep it. After that, John will extract one ball at random. What is the probability that John will extract a blue ball?

1) 1/3

2) 3/8

3) 1/2

4) 5/8

5) 11/16
SVP
Joined: 29 Aug 2007
Posts: 2453
Re: gmatclub test question : mary and john [#permalink]

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18 Mar 2009, 20:24
sanjay_gmat wrote:
The basket contains 3 white and 5 blue balls. Mary will extract one ball at random and keep it. After that, John will extract one ball at random. What is the probability that John will extract a blue ball?

1) 1/3
2) 3/8
3) 1/2
4) 5/8
5) 11/16

= (3/8) (5/7) + (5/8) (4/7)
= 35/56
= 5/8
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Senior Manager
Joined: 06 Jul 2007
Posts: 268
Re: gmatclub test question : mary and john [#permalink]

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19 Mar 2009, 00:36
GMAT TIGER wrote:
sanjay_gmat wrote:
The basket contains 3 white and 5 blue balls. Mary will extract one ball at random and keep it. After that, John will extract one ball at random. What is the probability that John will extract a blue ball?

1) 1/3
2) 3/8
3) 1/2
4) 5/8
5) 11/16

= (3/8) (5/7) + (5/8) (4/7)
= 35/56
= 5/8

Well, once Mary has picked up a ball, it should not have any affect on the probability of John's extracting a blue ball. Isn't it?
Director
Joined: 01 Apr 2008
Posts: 847
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: gmatclub test question : mary and john [#permalink]

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26 Mar 2009, 06:34
Hi Gmat tiger,
why do we add these two probabilites and not multiply?

GMAT TIGER wrote:
sanjay_gmat wrote:
The basket contains 3 white and 5 blue balls. Mary will extract one ball at random and keep it. After that, John will extract one ball at random. What is the probability that John will extract a blue ball?

1) 1/3
2) 3/8
3) 1/2
4) 5/8
5) 11/16

= (3/8) (5/7) + (5/8) (4/7)
= 35/56
= 5/8
CIO
Joined: 02 Oct 2007
Posts: 1209
Re: gmatclub test question : mary and john [#permalink]

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30 Mar 2009, 05:46
We add them because these two probabilities represent two scenarios, either of which will satisfy the condition.

The first one is that Mary will pick a white ball $$\left(P=\frac{3}{8}\right)$$ and then John will pick a blue one with the probability of $$\frac{5}{7}$$ (note that Mary keeps her white ball and John picks his from the 7 left, not 8).

The second scenario is that Mary picks a blue ball $$\left(P=\frac{5}{8}\right)$$ and John picks a blue ball with a probability of $$\frac{4}{7}$$.

We have to add the probabilities of both scenarios because either of them is good for us:

$$\frac{3}{8}*\frac{5}{7} + \frac{5}{8}*\frac{4}{7} = \frac{35}{56} = \frac{5}{8}$$

Hope this helps.
Economist wrote:
Hi Gmat tiger,
why do we add these two probabilites and not multiply?

GMAT TIGER wrote:
sanjay_gmat wrote:
The basket contains 3 white and 5 blue balls. Mary will extract one ball at random and keep it. After that, John will extract one ball at random. What is the probability that John will extract a blue ball?

1) 1/3
2) 3/8
3) 1/2
4) 5/8
5) 11/16

= (3/8) (5/7) + (5/8) (4/7)
= 35/56
= 5/8

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SVP
Joined: 29 Aug 2007
Posts: 2453
Re: gmatclub test question : mary and john [#permalink]

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31 Mar 2009, 21:16
Sorry guys I didnot review this post earlier.

Same explanation above/under:

dzyubam wrote:
We add them because these two probabilities represent two scenarios, either of which will satisfy the condition.

The first one is that Mary will pick a white ball $$\left(P=\frac{3}{8}\right)$$ and then John will pick a blue one with the probability of $$\frac{5}{7}$$ (note that Mary keeps her white ball and John picks his from the 7 left, not 8).

The second scenario is that Mary picks a blue ball $$\left(P=\frac{5}{8}\right)$$ and John picks a blue ball with a probability of $$\frac{4}{7}$$.

We have to add the probabilities of both scenarios because either of them is good for us:

$$\frac{3}{8}*\frac{5}{7} + \frac{5}{8}*\frac{4}{7} = \frac{35}{56} = \frac{5}{8}$$

Hope this helps.
Economist wrote:
Hi Gmat tiger,
why do we add these two probabilites and not multiply?

_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Re: gmatclub test question : mary and john   [#permalink] 31 Mar 2009, 21:16
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# gmatclub test question : mary and john

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