probability of success in experiment

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J.H

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An experiment is performed until it succeeds, the probability of success in experiment number n is 1 / (n+1)^2

What is the probability that you have succeeded for the first time in experiment number k, k = 1,2,3 ...?

I dont know how to solve this one, would appreciate some help :)
 
J.H said:
An experiment is performed until it succeeds, the probability of success in experiment number n is 1 / (n+1)^2

What is the probability that you have succeeded for the first time in experiment number k, k = 1,2,3 ...?

I dont know how to solve this one, would appreciate some help :)
Click to expand...
Please check the wording of your assignment. Make sure it is exact wording.

It says:
An experiment is performed until it succeeds, the probability of success in experiment number n is 1 / (n+1)^2​

Could the actual wording be:
An experiment is performed until it succeeds, the probability of success in trial number n is 1 / (n+1)^2​

Otherwise the interpretation is a bit awkward!!

Please answer the following also:

What is the probability that you have succeeded for the first time in trial #1?

What is the probability that you have failed in trial #1?
 
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J.H said:
An experiment is performed until it succeeds, the probability of success in experiment number n is 1 / (n+1)^2

What is the probability that you have succeeded for the first time in experiment number k, k = 1,2,3 ...?

I dont know how to solve this one, would appreciate some help :)
Click to expand...
What is the probability that you fail in the kth trial?

What is the probability that you fail in the first k-1 trials, and then succeed in the kth trial? That is what they are asking for.

If you still have trouble, try a specific case first. What is the probability that you fail on trials 1 and 2, and succeed on trial 3?
 
Subhotosh Khan said:
Please check the wording of your assignment. Make sure it is exact wording.

It says:
An experiment is performed until it succeeds, the probability of success in experiment number n is 1 / (n+1)^2​

Could the actual wording be:
An experiment is performed until it succeeds, the probability of success in trial number n is 1 / (n+1)^2​

Otherwise, the interpretation is a bit awkward!!

Please answer the following also:

What is the probability that you have succeeded for the first time in trial #1?

What is the probability that you have failed in trial #1?
Click to expand...

It should of course be formulated "the probability of success in trial number". Sry about that...
However, the probability of success the first time in trial #1 should simply be 1/4?

does this have any connection to the basel problem via Euler's Method (1+ 1/4 + 1/9 + 1/16+ ... = pi^2/6)?
 
J.H said:
It should of course be formulated "the probability of success in trial number". Sry about that...
However, the probability of success the first time in trial #1 should simply be 1/4?

does this have any connection to the basel problem via Euler's Method (1+ 1/4 + 1/9 + 1/16+ ... = pi^2/6)?
Click to expand...
Now calculate:

What is the probability that you have failed in trial #1? Then

What is the probability that you have succeeded for the first time in trial #2?
 
Subhotosh Khan said:
Now calculate:

What is the probability that you have failed in trial #1? Then

What is the probability that you have succeeded for the first time in trial #2?
Click to expand...
3/4

Right.. independent events ofc? The probability in trial #2 = 1/4 again
But how do I calculate everything? K is moving towards infinity, right?
 
Subhotosh Khan said:
How? Please share work!
Click to expand...
k=1 We have succeeded on the first attempt. (1/4) and the probability of failure is 3/4
k=2 means that you have failed for the first time and succeeded the second time (1/9) and the probability of failure is 8/9

k=3 that one failed 2 times and then succeeded on the third attempt, etc...
 
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