Doubt regarding Week 16 Quiz

I have a doubt reagarding some questions from the week 16 quiz.

Please see this question about transmitting bits. This was the solution given:


My doubt is … why aren’t we including the combination term in the probabilities? I mean why aren’t we multiplying 10C3 in P(X=3) ?

and similarly, here, in another problem,

Capture2

why aren’t we multiplying 20C19 in P(X=19) ?

Please reply.

Hi @prassannanandjha1,
If we look carefully, this question talks about geometric distribution.

And in a geometric distribution, we need not to choose a combination out of the given sequence, as only one combination is valid. (Which is: only the last bit has an error).
For more clarification, please refer to the formula for geometric distribution.

Could you please clarify why this is a geometric distribution and not a binomial distribution.
This is the question and answer for the 2nd part(the textile problem):

I am unable to figure out how this is a geometric distribution. We are clearly looking at ANY 18 out of 20 machines for P(X=18)

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Yes, this seems to be a discrepancy here… I’ve corrected this out.
The above clarification was in reference to the bits question.
Thanks for pointing.

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I have a query regarding a particular question “A set of n^2 objects…” in the week 16 quiz.
Here is the solution given on the website:

Please note that the last line has:
image
which should be equal to image .
This value is not same asimage as mentioned in the solution because 2^(n^2) is different from 4 n^2
Please look into the matter and rectify me if I am wrong.

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Hi @prassannanandjha1,
Sorry for that, this was just a confusion which occured due to a superscript tag error.
The option has been corrected now.
Thanks for pointing.

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can anybody explain the 2 consecutive head coin flip solution, it seems like we haven’t considered the case where first 2 coins or more than 2 coins came out as tail, why haven’t we added all those terms upto infinite?..and how are we able to equate expectation like that with failed attempts and their probability