A lot of 50 watches is known to have 10 defective watches. If 8 watches are selected one by one with a replacement at random, then the probability that there will be at least one defective watch is:

$1-(\frac{4}{5})^8$

The correct answer is Option (1) → $1-(\frac{4}{5})^8$

$P(\text{defective})=\frac{10}{50}=\frac{1}{5}$

$P(\text{non-defective})=\frac{4}{5}$

$P(\text{all 8 non-defective})=\left(\frac{4}{5}\right)^8$

$P(\text{at least one defective})=1-\left(\frac{4}{5}\right)^8$

The probability that at least one defective watch appears is $1-\left(\frac{4}{5}\right)^8$.