My Math Forum Binomial probability question

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September 26th, 2013, 01:03 AM   #1
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Binomial probability question

Hello,

The question I am having a problem with is as follows -

"A random group of dogs manage to to escape from an enclosure. Find the smallest number of dogs in the group if the probability that at least eight of the dogs in the group has less than four spots is greater than 0.99."

The probability distribution is given as X = number of spots, where X(2) = 0.3, X(3) = 0.4, X(4) = 0.23, X(5) = 0.05 and X(6) = 0.02. So Pr(less than four spots) = 0.7.

I have written the following inequality, but I don't think it can be solved.

[attachment=1:udorqyml]dogs.jpg[/attachment:udorqyml]

I answered a previous question which was similar, except it was a probability grater than 0.99 for at least one dog with less than four spots, not at least eight with less than four spots. Below is my working for that one. I'm hoping the working for both questions is similar and I'm just missing something.

[attachment=0:udorqyml]dogs0.jpg[/attachment:udorqyml]

Any assistance would be greatly appreciated.
Thank you,
- deSitter
Attached Images
 dogs.jpg (31.0 KB, 73 views) dogs0.jpg (53.6 KB, 73 views)

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