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NTA Abhyas JEE Main2020MathematicsProbabilityPractice

An exam consists of 3 problems selected randomly from a collection of 10 problems. For a student to pass, he needs to solve correctly at least two of three problems. If the student knows to solve exactly 5 problems, then the probability that the students pass the exam is

Options

  1. A1 2
  2. B1 3
  3. C3 4
  4. D5 6

Correct answer

A. 1 2

Step-by-step solution

Let A i be an event that student solve i problems correctly for i = 0 , 1 , 2 , 3 P A 2 ∪ A 3 = P A 2 + P A 3 ∵ Students knows to solve exactly 5 problems correctly P A 2 = 5 C 2 ×   5 C 1 10 C 3 , P A 3 = 5 C 3 10 C 3 P A 2 ∪ A 3 = 60 120 = 1 2

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