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#### zmogggggg

##### New Member
Re:

See "Bayes Theorem" and related posts on TalkStats. P(fault) = .05 = 1- P(no fault). P(favorable | no fault) = .8, P(favorable | fault) = .25. You seek P(fault|favorable).

:wave:

#### sahilkthr

##### New Member
We are looking for P (default / favorable) = 0.05 * 0.8 + 0.95 * 0.25 = 0.2775.

#### zmogggggg

##### New Member
What does Bayes Theorem tell you about P(fault|favorable)?

#### sahilkthr

##### New Member
Ok, my earlier answer was wrong, further study on Bayes theorem Gives me the following answer.

now let me know if its correct.. Am almost 100% sure that its correct...let me know if otherwise, thaks for your hints...

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#### sahilkthr

##### New Member
can i ask u for more questions, if you dont mind?

helloooooo

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#### sahilkthr

##### New Member
thanks, after this hint, i think i will be able to solve it, will post the correct answer for your verification

#### sahilkthr

##### New Member
1 more question

On an average 240 airplanes arrive in the O’Hare airport in an hour. What is the probability that
(i) at least one airplane arrives during a ten-minute time span?
(ii) No planes arrive during a 10-minute time span?
(iii) No more than four airplanes arrive during a ten-minute time span?

I think we have to use Poisson Distribution over here, but what is mean here for a 10 minute time span, not able to get it. can you provide me with the hint.

#### sahilkthr

##### New Member
zmoggggg can u provide hint for the following

On an average 240 airplanes arrive in the O’Hare airport in an hour. What is the probability that
(i) at least one airplane arrives during a ten-minute time span?
(ii) No planes arrive during a 10-minute time span?
(iii) No more than four airplanes arrive during a ten-minute time span?

I think we have to use Poisson Distribution over here, but what is mean here for a 10 minute time span, not able to get it. can you provide me with the hint.

#### zmogggggg

##### New Member
Re:

A nice thing about a Poisson random variable is that its intensity is dimensionally adjustable . lambda = L1/L2 = L1*a/L2*a = lambda2, and asking questions about a Poisson variable with intensity lambda is the same as with lambda2.

lambda = 40planes/10minutes -> P((X ~ Poisson(40/10)) >= 1). Repeat similar procedures for the other problems.

#### sahilkthr

##### New Member
so u mean to say that lambada is 40 for this particualr problem??. like 240 / 6 (for a 10 min time interval) is what we did, but using 40 as lambada, we arent able to derive any values from the table

#### zmogggggg

##### New Member
This thread's a bit long :O. Work on it and post answer if you'd like verification. You just need a calculator that can compute factorials and evaluate e^x to find poisson probabilities.

:wave:

#### sahilkthr

##### New Member
ok so lambada value here =4

and for the following question

a) atleast 1 plane arrives during the 10-minute time span, the answer is

P (x>=1) = 1 - P (x=0)

P(x=0) = (4^0 * e^-4) / 0! = 0.0183

P (x>=1) = 0.9817

can u verify if the answer is correct

Also, if you can make me more understand, that lambada for 10 minute time span should be 40, and when we calculate lambada=4, it is for a 1 minute time span, why cant we use lambada as 40, as the question is for a 10 minute time span. please explain