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NDA 2 2025 Maths, question 111

Topic: Probability

Q111

A fair coin is tossed 44 times. What is the probability that two heads do not occur consecutively?

  1. (a) 1/81/8
  2. (b) 3/83/8
  3. (c) 7/167/16
  4. (d) 1/21/2Correct answer

Solution.

Answer: (d) 1/21/2

  1. Out of 16 equally likely four-toss sequences, valid sequences have zero heads (1 way), one head (4 ways), or two nonadjacent heads (3 ways: positions 1&3,1&4,2&4).
  2. Three heads cannot avoid adjacency.
  3. Thus the probability is (1+4+3)/16=1/2.