Question:
For and initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any
problem is $\frac{4}{5}$, then the probability that he is unable to solve less than two problems is :
Correct Option: , 2
Solution:
Let $\mathrm{X}$ be random varibale which denotes number of problems that candidate is unbale to solve
$\because \mathrm{p}=\frac{1}{5}$ and $\mathrm{X}<2$
$\Rightarrow P(X<2)=P(X=0)+P(X=1)$
$=\left(\frac{4}{5}\right)^{50}+{ }^{50} \mathrm{C}_{1} \cdot\left(\frac{1}{5}\right) \cdot\left(\frac{4}{5}\right)^{49}$