1
$\begingroup$

suppose that a sample of size $n$ is to be chosen randomly (without replacement) from an urn containing $N$ balls, of which $m$ are white and $N-m$ are black. If we let $X$ denote the number of white balls selected, then the probability of getting exactly $i$ white balls is $$P(X=i)=\frac{\binom{m}i\binom{N-m}{n-i}}{\binom{N}{n}}, i=0,1,\ldots, \min(n,m).$$

Now the following probability $$\big(\frac{\binom{m}i\binom{N-m}{n-i}}{\binom{N}{n}}\big)^2$$ can be defined as: suppose I have two identical urns and two people doing the same experiment. Then the probability of both getting exactly $i$ white balls is $\big(\frac{\binom{m}i\binom{N-m}{n-i}}{\binom{N}{n}}\big)^2.$

Can anyone please give me reference of some examples (preferably from books available in online) where a probability is multiplied a number of times to represent replication of an experiment.

  • 0
    The probability of rolling a $6$ on a fair 6-sided die is $\frac{1}{6}$. The probability of rolling that die twice, each time turning up a $6$ is $\left( \frac{1}{6} \right)^2$. Is this the sort of example you're looking for? – 2017-02-05
  • 0
    @CodeLabMaster It is equivalent to: rolling two fair dice and getting $6$ on upper face of both dice. isn't it? If so, yes, this is the sort of example I am looking for. – 2017-02-05

0 Answers 0