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Please verify my solution to this problem.

Each of m urns contains three red chips and four white chips. A total of r samples with replacement are taken from each urn. What is the probability that at least one red chip is drawn from at least one urn?

Here is my solution:

$P$(at least one red chip is drawn from at least one urn)$=$
$1-P$(no red chip is drawn from any urn)$=$
$1-P$(only white chips are drawn from the urns)$=$
There is a $\tfrac47$ chance of drawing a white chip out of any one of the m urns.
Since it is replaced, there is an $(\frac47)^{r}$ chance of drawing a white chip for each of the r draws from any urn.
Therefore, $P$(draw at least one red chip from at least one urn) $=$ $1-(\frac47)^{m*r}$

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  • $\begingroup$ Where's your solution? $\endgroup$ – Shubham Johri Aug 2 at 4:17
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    $\begingroup$ It is very difficult to verify invisible solutions $\endgroup$ – Graham Kemp Aug 2 at 4:24
  • $\begingroup$ I'm new to the site. Now I realize that my solution is included in the question, not as an answer. $\endgroup$ – Dan Banaszak Aug 2 at 4:54
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Your working is fine.

The complement event is we do not see any red chips, which means that we only get white chips in all of the $m\cdot r$ trials.

Hence, the answer is $$1-\left( \frac47\right)^{m\cdot r}$$

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  • $\begingroup$ Thanks for feedback! $\endgroup$ – Dan Banaszak Aug 2 at 16:41

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