# For 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 problem is : Option 1)  $\frac{201}{5}\left ( \frac{1}{5} \right )^{49}$         Option 2) $\frac{316}{25}\left ( \frac{4}{5} \right )^{48}$ Option 3) $\frac{54}{5}\left ( \frac{4}{5} \right )^{49}$ Option 4) $\frac{164}{25}\left ( \frac{1}{5} \right )^{48}$

Probability of Sonning a  the problems out of 50 problems = $\frac{4}{5}$

$\Rightarrow P$ (not sonning ) =  $\frac{1}{5}$

The probability that he is unable to solve less than two problems is :

$P$ (zero correct ) + $P$ (one correct)

$\left ( \frac{1}{5} \right )^{50}+ ^{50}\textrm{C}_1 \left ( \frac{4}{5} \right )^{49}\left ( \frac{1}{5} \right )^{1}$

{using Binominal Probability)

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

Option 1)

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

Option 2)

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

Option 3)

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

Option 4)

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

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