Math Is Fun Forum

sassytonigirl

Member

Registered: 2016-01-24

Posts: 49

Elementary Statistics

Nine peas are generated from parents having the green/yellow pair of genes, so there is a 0.75 probability that an individual pea will have a green pod. Find the probability that among the 9 offspring peas, no more than 1 has a green pod. Is it unusual to get no more than 1 pea with a green pod when 9 offspring peas are generated? Why or why not?

The probability that no more than 1 of the 9 offspring peas has a green pod is ___________.
(Round to three decimal places as needed.)

Is it unusual to randomly select 9 peas and find that no more than 1 of them have a green pod? Note that a small probability is one that is less than 0.05.
A.  Yes, because the probability of this occurring is not small.
B.  Yes, because the probability of this occurring is very small.
C.  No, because the probability of this occurring is not small.
D.  No, because the probability of this occurring is very small. 

Can you help me with this?  I cannot even figure out how to set it up let alone get the answer.  PLEASE show me how to set it up and the answer.  This problem is due tuesday. 1/26/16

Thank you in advance.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Elementary Statistics

Hi;

I am getting a probability of 0 or 1 child having a green pod as 7 / 65536 = 0.0001068 so your answer is B.

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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.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Elementary Statistics

Hello,

I agree with bobbym. This is how you answer the problem:

The probability of any child having a green pod is 1/4 = 0.25. To have nine children with no green pods, this has to occur nine times. So you raise it to the ninth power.

For the probability of one green pod, no green pods has to occur eight times and a green pod has to occur once. Therefore we raise 1/4 to the eighth power and multiply it by 3/4. Furthermore, since there are nine different ways this can occur (the green pod could be possessed by any one of the nine children), we must also multiply this by 9.

When we add these together, we get 7/65536

Last edited by Relentless (2016-01-24 17:12:12)

sassytonigirl

Member

Registered: 2016-01-24

Posts: 49

Re: Elementary Statistics

I don't think I understand.  I am getting something very different.  This is what I am doing.  I am seeing that this is a cumulative binomial probability
distribution.  Because it states that "no more than" 1. we have to solve for P(x=0) and P(x=1) and then add those together. 

P= 0.75
N=9
X=1                                                       p(x=0) = 3.814697266
Q=0.25                                                  p(x=1) = 1.0299682      added together being 4.845 being the probability of no more than 1.   

setting it up like

p(x)= n!/(n-x)!x!  multiplied by p to the x power  and multiplied by q to the n-x power.

do this formula twice once with x equally 0 and once with x=1 and them the sum would be the probability of "no more than" 1 of the  offspring peas has a green pod.

This is all new to me so I know I could be WAY OFF but this is what I thought it was.  Am I wrong?

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Elementary Statistics

Hi, you are absolutely correct!

By the way, p(x=0) is two orders of magnitude smaller than p(x=1). So their sum is precisely 1.068115234375 * 10^-4. Perhaps this was the source of your confusion.
This probability is about one in 9362. I would call that a small probability (:

Last edited by Relentless (2016-01-25 15:54:31)

sassytonigirl

Member

Registered: 2016-01-24

Posts: 49

Re: Elementary Statistics

I got the question wrong.  said the answer was 0.000 so now i am REALLY CONFUSED!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Elementary Statistics

said the answer was 0.000

Did you leave something out over here at the end? You see, in probability 0 and .000102 are not quite the same things. 0 means that something can never happen while .000102 mean that it is rare but not impossible. Certainly, if someone said I had a .001%  chance of winning I would very much prefer that to saying I have 0%.

---

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.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Elementary Statistics

Hahaha, the answer is 0.000 to three decimal places... but you need to be completely accurate at every step for such small numbers

Fruityloop

Member

Registered: 2009-05-18

Posts: 143

Re: Elementary Statistics

Hi sassytonigirl,
   I'm not sure what you did but you put 1.0299682 instead of 0.00010299682. Always remember that the probability of an event occurring is always a number between 0 and 1.  Just keep trying. You can do it.

sassytonigirl

Member

Registered: 2016-01-24

Posts: 49

Re: Elementary Statistics

Thanks!!!!  Ill keep trying! 

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Elementary Statistics

Post when you have something.

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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.