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Help with a question in combinatorics

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Intern
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Joined: 17 May 2018
Posts: 15
Help with a question in combinatorics  [#permalink]

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New post 28 Sep 2018, 01:20
Hello, would much appreciate help with this kind of question :

there are 3 baskets, each with 5 balls.
in first basket we have 4 black balls, 1 yellow.
in second we have 3 black balls, 2 yellow.
in third we have 2 black , 3 yellow.
we pick one ball from each basket. what is the probability that we get at least one black ball ?

thanks
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Joined: 04 Dec 2015
Posts: 851
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Re: Help with a question in combinatorics  [#permalink]

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New post 01 Oct 2018, 12:20
1
Somnium wrote:
Hello, would much appreciate help with this kind of question :

there are 3 baskets, each with 5 balls.
in first basket we have 4 black balls, 1 yellow.
in second we have 3 black balls, 2 yellow.
in third we have 2 black , 3 yellow.
we pick one ball from each basket. what is the probability that we get at least one black ball ?

thanks


If you see language like 'at least one' in a probability problem, this strategy will usually work. Instead of finding the probability of getting one black ball, then two black balls, then three black balls, you can actually just find the probability of getting all yellow balls, and subtract from 1. You can do that because you're basically looking for the probability that anything other than all yellow is what happens. That'll be the 'opposite' of the probability that you get all yellow.

The probability of getting all yellow balls is 1/5 * 2/5 * 3/5 (the product of the probability of getting a yellow ball from each basket). That equals 6/125.

So, the probability of getting at least one black (in other words, NOT getting all yellow) is 1-6/125 or 119/125.
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Joined: 23 Nov 2017
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Location: Singapore
Concentration: Strategy, Other
Re: Help with a question in combinatorics  [#permalink]

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New post 28 Sep 2018, 01:28
Somnium wrote:
Hello, would much appreciate help with this kind of question :

there are 3 baskets, each with 5 balls.
in first basket we have 4 black balls, 1 yellow.
in second we have 3 black balls, 2 yellow.
in third we have 2 black , 3 yellow.
we pick one ball from each basket. what is the probability that we get at least one black ball ?

thanks



Is the answer 119/125 ?
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Joined: 19 Oct 2013
Posts: 511
Location: Kuwait
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WE: Engineering (Real Estate)
GMAT ToolKit User
Re: Help with a question in combinatorics  [#permalink]

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New post 28 Sep 2018, 01:43
Somnium wrote:
Hello, would much appreciate help with this kind of question :

there are 3 baskets, each with 5 balls.
in first basket we have 4 black balls, 1 yellow.
in second we have 3 black balls, 2 yellow.
in third we have 2 black , 3 yellow.
we pick one ball from each basket. what is the probability that we get at least one black ball ?

thanks


Happen to have the answer choices? What is the source for this question?
Intern
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Joined: 17 May 2018
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Help with a question in combinatorics  [#permalink]

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New post 28 Sep 2018, 03:33
in one of official CATs , but unfortunately I don't remember the exact data that was there so I don't know what the answer should be. I changed the stats a bit..
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Help with a question in combinatorics   [#permalink] 28 Sep 2018, 03:33
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