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NTA Abhyas JEE Main2020MathematicsProbabilityPractice

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 4 5 , then the probability that he is unable to solve less than two problems is

Options

  1. A201 5 1 5 49
  2. B164 25 1 5 48
  3. C316 25 4 5 48
  4. D54 5 4 5 49

Correct answer

D. 54 5 4 5 49

Step-by-step solution

Let, X = number of questions student is unable to solve. p = P   (the student answers a question correctly) = 4 5 ⇒   q = 1 - p = 1 5 (probability that the student does not answer a question correctly) Also, n = 50 (Total number of question) Hence, required probability: P ( X < 2 )   = P X = 0 + P X = 1 =   50 C 0   4 5 50 +   50 C 1 4 5 49 1 5 = 54 5   4 5 49

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