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A fair coin is tossed 4 times. What is the probability that two heads do not occur consecutively?

Options

  1. A1/8
  2. B3/8
  3. C7/16
  4. D1/2

Correct answer

D. 1/2

Step-by-step solution

Total number of possible outcomes when a fair coin is tossed 4 times is 2^4 = 16 . Let E be the event that two heads do not occur consecutively. The favorable outcomes are the sequences of length 4 that do not contain 'HH'. We can count these by the number of heads in the sequence: Case 1: 0 heads TTTT ( 1 outcome) Case 2: 1 head HTTT, THTT, TTHT, TTTH ( 4 outcomes) Case 3: 2 heads To avoid consecutive heads, the heads must be separated by tails. The possible arrangements are HTHT, HTTH, THTH ( 3 outcomes) Case 4:

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