In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is
(A) ${10^{ - 1}}$
(B) ${\left( {\cfrac{1}{2}} \right)^5}$
(C) ${\left( {\cfrac{9}{{10}}} \right)^5}$
(D) $\cfrac{9}{{10}}$
Option C is correct
$p$ , the probability of defective bulb $= \cfrac{{10}}{{100}} = \cfrac{1}{{10}}$
$\Rightarrow$ $q = 1 - \cfrac{1}{{10}} = \cfrac{9}{{10}}$ and $n = 5$
Now, $P(X = 0){ = ^5}{C_0}{q^5}{p^0} = (1){\left( {\cfrac{9}{{10}}} \right)^5}(1) = {\left( {\cfrac{9}{{10}}} \right)^5}$
NCERT & Exemplar solution for CBSE Class 12 Mathematics, Probability. Curated by Sachin Sharma. Free for all students.