# Combinatorics & Binomial Probability

• Nov 8th 2011, 09:30 PM
Jaytohkay
Combinatorics & Binomial Probability
Hi all, I'm having troubles figuring out how to answer these questions and similar questions.

Combinatorics
In the long run 40% of patients treated for a particular disease with the drug streptomycin are cured. If a doctor were to treat 10 randomly chosen patients with the drug, what is the probability of:
i) 6 cures
ii) more than 8 cures?

A second doctor treats 10 patients with a new treatment and obtains 6 cures. Comment on this result.

And

A management team consists of 12 people. In how many ways could a sub-committee of 4 people be formed?

Thirty-two students are to be interviewed for 8 different jobs. In how many ways could the jobs be filled by selecting from these applicants.

Binomial Probability

A printer which has been giving trouble produces an error message on 3 out of every 10 print jobs on average.

What is the probability of this printer successfully doing 4 print jobs in a row?

Find the probability of drawing 2 red tokens from a box containing 5 red, 3 white and 5 yellow tokens. The tokens are drawn one at a time without replacement?

Thanks a lot.
• Nov 8th 2011, 09:38 PM
pickslides
Re: Combinatorics & Binomial Probability
Quote:

Originally Posted by Jaytohkay
In the long run 40% of patients treated for a particular disease with the drug streptomycin are cured. If a doctor were to treat 10 randomly chosen patients with the drug, what is the probability of:
i) 6 cures
ii) more than 8 cures?

Apply the fact that $\displaystyle P(x=k) = \binom{n}{k}\times p^k\times (1-p)^{n-k}$

You have p = 0.4 and n=10

find

$P(x=6)$

and

$P(x\geq 8) = P(x= 8)+P(x=9)+P(x=10)$
• Nov 8th 2011, 10:04 PM
Jaytohkay
Re: Combinatorics & Binomial Probability
Thanks for the help, but I don't understand those formulas or how to use them, could you please explain a bit more as I'm having trouble interpreting them.
• Nov 8th 2011, 10:21 PM
pickslides
Re: Combinatorics & Binomial Probability
Which bit do you not understand?
• Nov 8th 2011, 10:28 PM
Jaytohkay
Re: Combinatorics & Binomial Probability
Quote:

Originally Posted by pickslides
Which bit do you not understand?

I've never seen a formula like it before as I rarely deal with them at my level of math. So I don't know how to interpret it correctly.

How I'm seeing the first bit is

You have p = 0.4 and n=10
P(.4) = (10/.4(25)

Then I just don't understand the rest.