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}

 

Answers (1)

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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