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GATE 2023 CS – Question 53

Engineering Mathematics · Probability and Statistics · 2 marks · Multiple select

Consider a random experiment where two fair coins are tossed. Let A be the event that denotes HEAD on both the throws, B be the event that denotes HEAD on the first throw, and C be the event that denotes HEAD on the second throw. Which of the following statements is/are TRUE?

  1. A and B are independent.
  2. A and C are independent.
  3. B and C are independent.
  4. Prob(B|C) = Prob(B)

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Show answer and explanation

Correct answer: (C) B and C are independent.; (D) Prob(B|C) = Prob(B)

Explanation

P(A∩B)=1/4 ≠ P(A)P(B)=1/8, so A,B are dependent, and likewise A,C. B and C concern different tosses, so P(B∩C)=1/4=P(B)P(C). Hence they are independent and P(B|C)=P(B).