JEE MainMathematicsModerateProbability

For an 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 [IMAGE],then the probability that he
is unable to solve less than two problems is

Show answer and solution

There are 50 questions in an exam.
Probability of each question to be correct =

= p = \frac{4}{5}

probability of each question is incorrect

= q = \frac{1}{5}

Let X= number of correct question in 50 questions.
Hence required probability

= \left( \frac{4}{5} \right)^{50} + \ ^{50}C_{1}\left( \frac{1}{5} \right)\left( \frac{4}{5} \right)^{49}

= \left( \frac{4}{5} \right)^{49}\left( \frac{4}{5} + 10 \right)\left( \frac{4}{5} \right) = \frac{54}{5}\left( \frac{4}{5} \right)^{49}

Source: Grass-G / M-28 Mathematics Paper FST 16 Jan.docx

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