The GATE Grind

GATE 2024 DA – Question 12

Probability and Statistics · Counting, probability axioms, conditional probability and Bayes theorem · 1 mark · Multiple choice

Three fair coins are tossed independently. T is the event that two or more tosses result in heads. S is the event that two or more tosses result in tails.

What is the probability of the event $T \cap S$ ?

  1. 0
  2. 0.5
  3. 0.25
  4. 1

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Show answer and explanation

Correct answer: (A) 0

Explanation

With only three tosses, two or more heads means at most one tail, and two or more tails means at most one head. Both cannot happen together (that would need at least 4 tosses), so $T \cap S$ is empty and its probability is 0.