Math Is Fun Forum

mom

Member

Registered: 2012-04-25

Posts: 94

Probability again

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?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability again

Hi;

Did you draw a Venn diagram?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

mom

Member

Registered: 2012-04-25

Posts: 94

Re: Probability again

no??

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability again

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

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Probability again

Why do you need a venn diagram to do that?

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability again

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

mom

Member

Registered: 2012-04-25

Posts: 94

Re: Probability again

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?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Probability again

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

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mom

Member

Registered: 2012-04-25

Posts: 94

Re: Probability again

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

OzMark

Member

Registered: 2013-06-10

Posts: 9

Re: Probability again

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)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Probability again

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

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability again

Hi;

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

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.