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KVPY2017MathematicsProbability

If a fair coin is tossed 5 times, the probability that heads does not occur two or more times in a row is

Options

  1. A12 2⁵
  2. B13 2⁵
  3. C14 2⁵
  4. D15 2⁵

Correct answer

B. 13 2⁵

Step-by-step solution

Case (1): All tail ( 1 2 )⁵ Case (2): 4 ~T , 1 H ⁵ C ₄ ( 1 2 )⁴ ( 1 2 )⁵= 5 2⁵ Case (3): T T T ( 1 2 )³ ⁴ C ₂ ( 1 2 )²= 1 2⁵ 6= 6 2⁵ Case (4): T T ( 1 2 )² ( 1 2 )³= 1 2⁵ overall 13 2⁵

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