Ten eggs are drawn successively with replacement from a lot containing 10% defective eggs. The probability that there is at least one defective egg is
Answer & explanation
Correct answer: option 1
Probability of defective eggs =10%
$P=\frac{10}{100}=\frac{1}{10}$
Let the (Probability of good eggs) = q
$q=1-p=1-\frac{10}{100}=\frac{100-10}{100}=\frac{90}{100}=\frac{9}{10}$
(Probability of at least one egg defective out of 10) ⇒ p(1) + p(2) + p(3)+...
$=[p(0)+p(1)+p(2)+...+p(10)−p(0)$
$=1-P(0)=1-(\frac{9}{10})^{10}⇒\frac{10^{10}-9^{10}}{10^{10}}$.
So option 1 is correct.