1. ## Probability Questions

The probability of a french hen truly having citizenship is .81, find the probability that exactly 2 hens out of three have citizenship.

and

If there is an infinite number of calling birds, and the probability of a bird actually calling is .63, find the probability of finding the first calling bird on the third attempt.

Please solve and then explain. Thanks!

2. Originally Posted by suchgreatheights

The probability of a french hen truly having citizenship is .81, find the probability that exactly 2 hens out of three have citizenship.
Use the binomial distribution

$\displaystyle \displaystyle P(2) = ^3C_2(0.81)^2\times (1-0.81)^1=\dots$

3. Originally Posted by suchgreatheights

The probability of a french hen truly having citizenship is .81, find the probability that exactly 2 hens out of three have citizenship.
Let X be the random variable that represents the number of french hens truly having citizenship. Then X has a binomial distribution with n=3 and p=.81. Now what is P(X=2)?

If there is an infinite number of calling birds, and the probability of a bird actually calling is .63, find the probability of finding the first calling bird on the third attempt.

Please solve and then explain. Thanks!
This one is a little more interesting because you're looking for the first success after so many trials. Hence, this one is modeled by a geometric distribution where p=.63. Now what is P(X=3)?

I leave it to you to look up their corresponding pdfs and finish working out these problems. Can you proceed?

4. Well, what would be setup of the geometric distribution for the second one?

5. P(failure on first)P(failure on second)P(success on third attempt)

=(.37)(.37)(.63)

assuming indep between these selections