A lot of 100 watches is known to have 10 defective watches.
If 8 watches are selected (one by one with replacement) at random, then what is the probability that there will be atleast one defective watch?

Probability of defective watch from a lot of 100 watches $= \frac{{10}}{{100}} = \frac{1}{{10}}$

$\therefore$ $p = 1/10,q = \frac{9}{{10}},n = 8$ and $r \ge 1$

$\therefore$ $P(r \ge 1) = 1 - P(r = 0) = 1{ - ^8}{C_0}{\left( {\frac{1}{{10}}} \right)^0}{\left( {\frac{9}{{10}}} \right)^{8 - 0}}$

$= 1 - \frac{{8!}}{{0!8!}} \cdot {\left( {\frac{9}{{10}}} \right)^8} = 1 - {\left( {\frac{9}{{10}}} \right)^8}$