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Previous Year Question (PYQs)

A coin is thrown 8 number of times. What is the probability of getting a head in an odd number of throw?




Solution

Total outcomes = \( 2^8 = 256 \)

Favorable outcomes (odd heads):

  • \( \binom{8}{1} = 8 \)
  • \( \binom{8}{3} = 56 \)
  • \( \binom{8}{5} = 56 \)
  • \( \binom{8}{7} = 8 \)

Total favorable = \( 8 + 56 + 56 + 8 = 128 \)

So, Probability = \( \frac{128}{256} = \boxed{\frac{1}{2}} \)

? Final Answer: \( \boxed{\frac{1}{2}} \)


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