# Thread: Probability of drawing marbles 15 trials

1. ## Probability of drawing marbles 15 trials

If a bag contains 3 purple, 2 red, and 5 blue marbles, what is the probability of drawing a purple marble 6 or more times out of 15 trials?

I am having the hardest time approaching this question. Could someone show the steps of solving this problem? Thanks!

2. ## Re: Probability of drawing marbles 15 trials

Given that there are only 10 marbles I assume you are replacing the marbles after selecting them, yes?

If so then this is just a binomial distribution with $n=16,~p = \dfrac {3}{10}$

$P[k] =\displaystyle \binom{15}{k} \left(\dfrac{3}{10}\right)^k \left(\dfrac{7}{10}\right)^{15-k}$

$P[\text{6 or more}] = 1 - P[\text{5 or less}] = 1 - \displaystyle \sum_{k=0}^5~ \binom{15}{k} \left(\dfrac{3}{10}\right)^k \left(\dfrac{7}{10}\right)^{15-k} = 1-I_{\frac {7}{10}}(10,6)$

where $I_x(a,b)$ is the regularized incomplete beta function

3. ## Re: Probability of drawing marbles 15 trials

Yes, I believe so! Thank you! How do you compute this calculation exactly- what would I put in my calculator?

4. ## Re: Probability of drawing marbles 15 trials

Originally Posted by illusiveman
Yes, I believe so! Thank you! How do you compute this calculation exactly- what would I put in my calculator?
well.. I don't know what calculator you've got...

$\displaystyle \binom{n}{k} = \dfrac{n!}{k!(n-k)!}$

I assume you know how to raise a number to a power on the thing.

That's all you need. You might want to use excel or something if you've got it.

There are probably some online resources that would allow you to calculate this

for that matter you can just do this

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5. ## Re: Probability of drawing marbles 15 trials

Thank you so much!