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I quote the question:

In some cultures, it is important to have at least one son. The plan is to have children until one son is born. Find the PDF of the number of daughters in a family. The success rate of having a son is p.

My first approach:

Bernoulli experiment

let D = number of daughters. Then d+1 experiments with d successes have been performed.

$f_D(d) = {d +1 \choose d} (1-p)^d p^1 = (d+1) (1-p)^d p$

This is apparently wrong. The answer should be

$f_D(d) = (1-p)^d p$

Why is my approach not correct and what is a correct approach then?

Improve this question
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    $\begingroup$ HINT: What is the interpretation of the combinatorial term in the first density you have provided? What exactly is the interpretation of that probability? How is the ordering of events accounted for? $\endgroup$
    – AdamO
    Commented Jun 21, 2014 at 18:44
  • $\begingroup$ @AdamO Hmm yes. The binomial coefficient respresents the number of possible ways to achieve the end result. And in this case there is only one way to achieve it. DDDDDDDDS – $\endgroup$
    – tgoossens
    Commented Jun 21, 2014 at 18:50
  • $\begingroup$ Closely related question here $\endgroup$
    – Glen_b
    Commented Jun 22, 2014 at 2:07
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    $\begingroup$ Would you like to write your understanding up into an answer? $\endgroup$
    – Glen_b
    Commented Jun 22, 2014 at 2:10
  • $\begingroup$ I edited your title to replace "amount of" with "number of" since failures are things you count rather than measure, and I replace PDF with probability function since it's discrete - so the word 'density' doesn't apply. Your question is actually about the number of trials rather than the number of failures, but I didn't make that change (you may wish to, however). $\endgroup$
    – Glen_b
    Commented Jun 22, 2014 at 2:16

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