# For and initial screening of an admission test,

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 :

1. $\frac{316}{25}\left(\frac{4}{5}\right)^{48}$

2. $\frac{54}{5}\left(\frac{4}{5}\right)^{49}$

3. $\frac{164}{25}\left(\frac{1}{5}\right)^{48}$

4. $\frac{201}{5}\left(\frac{1}{5}\right)^{49}$

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 $\mathrm{X}<2$

$\Rightarrow P(X<2)=P(X=0)+P(X=1)$

$=\left(\frac{4}{5}\right)^{50}+{ }^{50} \mathrm{C}_{1} \cdot\left(\frac{1}{5}\right) \cdot\left(\frac{4}{5}\right)^{49}$