There are $n$ balls in a bag. if two drawings are made in succession drawing one ball at a time with replacement, it is found that both are white. Find probability that 3rd drawing is also white.

Since first two drawings are white balls. we can conclude that bag contains minimum one white ball and maximum $n$ white balls.

so assuming there are $r$ white balls and $n-r$ black balls

we have $r \ge 1$

so probability that 3rd drawing is also white is given by

$\frac{r}{n}$ but how to get answer in terms of $n$

  • 2
    $\begingroup$ You are going to need a prior distribution for the number of white balls $R$. One possibility might be uniform; another might be binomial; and there are others $\endgroup$ – Henry May 9 '17 at 4:57
  • $\begingroup$ ok can you elaborate more please $\endgroup$ – Umesh shankar May 9 '17 at 4:59
  • 1
    $\begingroup$ If there is replacement, then the third draw is independent of the first and second drawings. Like you said we know that there is at least one white ball. So one thing for certain is the probability is in the closed interval $ [1/n, 1] $ $\endgroup$ – WaveX May 9 '17 at 5:08
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    $\begingroup$ You can't have an answer exclusively in terms of $n$. $\endgroup$ – Peter May 9 '17 at 9:48

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