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**mom****Member**- Registered: 2012-04-25
- Posts: 94

I am stuck again. I have:

Out of 250 third grade boys, 130 played baseball, 130 played soccer, and 60 played both. Find the probability that a boy chosen at random did not play either sport.

Consider event E, which is "a chosen boy satisfies the requirements". The probability of E is determined by the following formula.

Pr(E)=[number of outcomes in E]/N

Where the total number of outcomes N is equal to the number of boys. So the numerator is the number of boys who satisfy the requirements and the denominator is the total number of boys.

Let A be the set of boys who play baseball, N(A) - number of boys who play baseball and B be the set of boys who play soccer, N(B) - number of boys who play soccer.

So, from the problem statement N(A)=130, N(B)=130,N(A and(upside down U) B)=60.

to find the probability that a boy chosen at random did not play either sport we should divide the number of such boys by the total number of boys. What is the number of boys who don't play either sport?

The answer is 50 but I don't know how to get to that answer. This is where I am lost so far. Can you please assist?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

Hi;

Did you draw a Venn diagram?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**mom****Member**- Registered: 2012-04-25
- Posts: 94

no??

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

We have 70 playing just baseball + 70 playing just soccer and 60 playing both. 70 + 70 + 60 = 200. The only thing left is those not doing any of that. 250 - 200 = 50.

Go here:

http://www.purplemath.com/modules/venndiag4.htm

http://www.mathsisfun.com/sets/venn-diagrams.html

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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Why do you need a venn diagram to do that?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

Experimental math! When you get jumbled up as I do sometimes, I go to pictorial images because that is what the human mind understands best. It is part of the strategy of always coming up with an answer, even if wrong! An answer has a chance of being right. A blank page is never right.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**mom****Member**- Registered: 2012-04-25
- Posts: 94

Bobby,

The diagrams help tremendously but I am still drawing a blank for some reason. I did figure the following from using the visual.

250 boys, 120 play baseball, 130 play soccer, 60 play both.

Did not play either sport: 60+60+70=190 250-190=60 60/250=.24 probability

play exactly one sport: 60+70=130/250=.52 probability

play soccer but not baseball: 70/250=.28 probability

play soccer, given that he played baseball: 60/120=.50

played baseball, given that he did not play soccer: 60/120=.50

did not play baseball, given that he did not play soccer: the answer is .46 but for some reason, I can not visualize what to do in order to come to that conclusion. Could you please help?

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,378

hi Mom

All those answers look correct to me.

The last one?

n(did not play soccer) = 250 - 130 = 120

n(of those 120 who did not play baseball) = 60 (make sure you are only counting the not baseballs out of the not soccers)

P = 60/120

P(did not play baseball given did play soccer) = 60/130 = 0.461.....

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**mom****Member**- Registered: 2012-04-25
- Posts: 94

wow!! finally got my brain to work properly. I got it figured out. thanks

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**OzMark****Member**- Registered: 2013-06-10
- Posts: 9

Hello,

Bob Bundy, I think your Venn diagram is slightly wrong,

it should be 70-60-70 and 50 play no sport (your diagram says 60-60-70 and 60 play no sport)

BobbyM,I think your Venn diagram is correct, you could add that the play no sports guys are 50

Do not play either sport 50/250 = 0.200

Play exactly one sport 140/250 = 0.560

Play soccer not baseball 70/250 = 0.280

Play soccer given that he play baseball 60/130 = 0.461 (actually 0.46154)

Play baseball given that he did not soccer 70/120 = 0.583

did not play baseball (50), given that he did not play soccer(120) = 50/120 = 0.461 (actually 0.41666)

*Last edited by OzMark (2013-06-11 13:10:34)*

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,378

hi OzMark,

Thanks for your input.

I assumed post 7 was for a new question. My diagram works for the information given there.

bobbym's diagram and your figures are for the information in post 1. So now I'm confused.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

Hi;

The confusion is post #7. I think she meant 130 not 120. Anyway, 50 is for post #1.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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