Expert: Paul Klarreich - 10/13/2007

Question
Hey Paul,

I have been having trouble with a couple of problems. If you dont mind taking a look that would be great.

Thanks,
Eric
\

1.  For a binomial distribution, compare P(x = 3) when n = 10 and p = .4 to P(x
= 7) when n = 10 and p = .6.



2.  Consider a Poisson probability distribution in a process with an average of
3 flaws every 100 feet.  Find the probability of no flaws in 100 feet.  

Answer
Questioner:   Eric
Category:  Advanced Math
Private:  No
 
Subject:  Probability Question
Question:  Hey Paul,

I have been having trouble with a couple of problems. If you dont mind taking a

look that would be great.

Thanks,
Eric
........................................
Hi, Eric,

1.  For a binomial distribution, compare P(x = 3) when n = 10 and p = .4 to P(x
= 7) when n = 10 and p = .6.

..........................
First one: P(x = 3) when n = 10 and p = .4

P(x = 3) = C(10,3) p^3 (1-p)^7

P(x = 3) = C(10,3) (0.4)^3 (0.6)^7

. . . . . . . . . . . . . . . .
Second one: P(x = 7) when n = 10 and p = .6

P(x = 7) = C(10,7) p^7 (1-p)^3

P(x = 7) = C(10,7) (0.6)^7 (0.4)^3

But  C(10,7) = C(10,3) -- basic property of binomial coefficients -- so these two

probabilities look the same to me.
.....................................
2.  Consider a Poisson probability distribution in a process with an average of
3 flaws every 100 feet.  Find the probability of no flaws in 100 feet.
...............
Sorry -- this one is beyond my recollection and I can't help you with it.