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Manipal MET2022MathematicsProbability

A multiple choice examination has 5 questions. Each question has 4 alternative answer of which exactly one is correct. The probability that a student will get 4 or more correct answer just by guessing is

Options

  1. A1 4^5
  2. B( 3 4 )^4
  3. C1 4^3
  4. D3 4^5

Correct answer

C. 1 4^3

Step-by-step solution

Probability of guessing a correct answer, p= 1 4 and probability of guessing a wrong answer q= 3 4 So, the probability of guessing 4 or more correct answer aligned P(X 4) & = ^5 C₄ ( 1 4 )^4 ( 3 4 )+ ^5 C₅ ( 1 4 )^5 & =5 1 4^4 3 4 + 1 4^5 & = 15 4^5 + 1 4^5 = 16 4^5 = 4^2 4^5 = 1 4^3 aligned

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