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Old July 8th, 2010, 07:52 PM
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Default Probabilities....

Everybody,

I recently encountered a problem in that drew quite a bit of discussion on another web site, and thought some here might enjoy wrestling with it.

First, the simpler problem that came into the discussion. You know that a man has two children, and that at least one of his children is a son. What is the probability that he has two sons?

Now, the problem originally posted on the other site. You know that a man has to children, and that at least one of his children is a son who was born on a Thursday. What is the probability that he has two sons?

For both problems, assume a child of either sex and birth on each day of the week to be equiprobable.

I have managed to dig up with prizes for whoever posts the first correct solutions to these problems. The order of posting will determine the winner. My determination of correctness will be final.

>> Whoever posts the first correct solution to the simpler problem will receive a small medallion struck in a copper alloy bearing, on its obverse, the likeness of a former President.

>> Whoever posts the first correct solution to the original problem will receive a somewhat larger medallion clad on both sides with a silver alloy, also bearing, on its obverse, the likeness of a former President.

I'll present each medallion in person whenever it's opportune to do so. Unfortunately, there's no budget for travel to present these awards.

Norm.
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Old July 9th, 2010, 08:11 AM
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The answer to both questions if 50%.
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A Bad Day At Sea [with power] Always Beats A Good Day At Work
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Old July 9th, 2010, 12:15 PM
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Actually I rethought it (and couldn't edit my response).

The correct answer is 66%
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A Bad Day At Sea [with power] Always Beats A Good Day At Work
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Old July 9th, 2010, 05:28 PM
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Bob,

Quote:
Originally Posted by You
Actually I rethought it (and couldn't edit my response).

The correct answer is 66%
Only to the first, if you truncate (rather than rounding) to two digits.

But in any case, you need to post solutions rather than answers to qualify for the prizes.

Norm.
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Old July 9th, 2010, 06:19 PM
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Lost me...
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Old July 12th, 2010, 08:53 AM
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Okay - final answer 33.33%
With two children there are four possibilities:
BG
GB
BB
GG

Given that at least one child is a boy that eliminates that last choice. So the two children are either, BG, GB, and BB. The chance that both are boys is 1:3 or 33.33%
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A Bad Day At Sea [with power] Always Beats A Good Day At Work
Carnival: Glory 2004, Destiny 2008, Splendor 2009, Freedom 2011, Valor 2012, Dream 2013
Celebrity: Summit 2011
Princess: Ruby 2010, 2014, Caribbean 2013, Coral 2014, Regal 2014
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Old July 12th, 2010, 06:17 PM
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Bob,

Quote:
Originally Posted by You View Post
Okay - final answer 33.33%
With two children there are four possibilities:
BG
GB
BB
GG

Given that at least one child is a boy that eliminates that last choice. So the two children are either, BG, GB, and BB. The chance that both are boys is 1:3 or 33.33%
You are first with the correct solution to the simpler problem, and thus earned the copper alloy medallion -- which I'll present whenever we meet!

That's not the correct solution to the original problem, though.

The larger medallion clad with silver alloy is still up for grabs....

Norm.
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