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A couple decides to have 4 children. If they succeed in havi

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Re: A couple decides to have 4 children. If they succeed in havi  [#permalink]

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New post 02 Apr 2019, 07:58
EMPOWERgmatRichC wrote:
shavarna wrote:
I thought that order does not matter for when child is born, therefore
Total number of events = 5 (explained below)

0 Boys 4 Girls
1 Boy 3 Girls
2 Boys 2 Girls
3 Boys 1 Girl
4 Boys 0 Girl

Probability (2 B and 2 G exactly) = 1/5

Not sure where I am assuming and making a mistake.


Hi shavarna,

The 5 options you've listed are NOT all equally likely, so you would have to do a bit more work to get to the correct answer. There are a couple of ways to answer this question:

1) You could make a table of all the options (since each child could be a boy or a girl, there are only 2^4 = 16 possible outcomes) and determine all the ways to get 2 boys and 2 girls

or

2) You can do the math

Here's the math approach:

Since each child has an equal chance of ending up as a boy or girl, there are 2^4 possibilities = 16 possibilities. It also doesn't matter which 2 of the 4 children are boys, so you can treat this part of the question as a combination formula question...

4c2 = 4!/[2!2!] = 6 ways to get 2 boys and 2 girls out of 16 possibilities. 6/16 = 3/8

Final Answer =

GMAT assassins aren't born, they're made,
Rich


Hi EMPOWERgmatRichC, chetan2u,

But that's also valid method right as nowhere stated in question that in how many different way this is possible.
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Re: A couple decides to have 4 children. If they succeed in havi  [#permalink]

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New post 02 Apr 2019, 12:09
Hi Gmatprep550,

The question asks for the PROBABILITY that exactly 2 of the 4 children are boys, so the total number of possible outcomes IS a factor in this question.

If you describe the 5 possible outcomes as...
0 Boys 4 Girls
1 Boy 3 Girls
2 Boys 2 Girls
3 Boys 1 Girl
4 Boys 0 Girl

...then you might think that there is a 1/5 chance of having 2 boys and 2 girls, but that is NOT mathematically correct (since the 5 possible outcomes do NOT all have an equal likelihood of occurring).

GMAT assassins aren't born, they're made,
Rich
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Re: A couple decides to have 4 children. If they succeed in havi  [#permalink]

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New post 02 Apr 2019, 12:21
EMPOWERgmatRichC wrote:
Hi Gmatprep550,

The question asks for the PROBABILITY that exactly 2 of the 4 children are boys, so the total number of possible outcomes IS a factor in this question.

If you describe the 5 possible outcomes as...
0 Boys 4 Girls
1 Boy 3 Girls
2 Boys 2 Girls
3 Boys 1 Girl
4 Boys 0 Girl

...then you might think that there is a 1/5 chance of having 2 boys and 2 girls, but that is NOT mathematically correct (since the 5 possible outcomes do NOT all have an equal likelihood of occurring).

GMAT assassins aren't born, they're made,
Rich


Thanks EMPOWERgmatRichC
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Re: A couple decides to have 4 children. If they succeed in havi  [#permalink]

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New post 10 Nov 2019, 10:01
Why is it a permutation problem? Why does the sequence matter here?

If it’s asking for a possibility where there are exactly 2 boys and 2 girls.

BBGG
If the sequence doesn’t matter, it’s just 1

Out of

BBGG
BGGG
GGGG
BBBB
GBBB

I got 1/5.

Posted from my mobile device
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Re: A couple decides to have 4 children. If they succeed in havi  [#permalink]

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New post 11 Nov 2019, 15:03
Hi Seriousthistime,

I discussed this issue in a series of posts directly above yours. The question asks for the PROBABILITY that exactly 2 of the 4 children are boys, so the total number of possible outcomes IS a factor in this question.

If you describe the 5 possible outcomes as...
0 Boys 4 Girls
1 Boy 3 Girls
2 Boys 2 Girls
3 Boys 1 Girl
4 Boys 0 Girl

...then you might think that there is a 1/5 chance of having 2 boys and 2 girls, but that is NOT mathematically correct (since the 5 possible outcomes do NOT all have an equal likelihood of occurring). For example, with 4 children - and an equal probability of having a boy or a girl - there are 2^4 = 16 possible outcomes. The "all girls" and "all boys" outcomes occur just ONCE each (out of those 16). The "two boys and two girls" outcome occurs 6 times.

GMAT assassins aren't born, they're made,
Rich
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Re: A couple decides to have 4 children. If they succeed in havi   [#permalink] 11 Nov 2019, 15:03

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