Multiple choice

An unbiased coin is tossed $n$ times. The probability that head will present itself, odd number of times is

  1. $\dfrac{1}{4}$
  2. $\dfrac{1}{3}$
  3. $\dfrac{1}{2}$
  4. $\dfrac{1}{5}$
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C Correct answer
Explanation

The probability of an odd number of heads in n tosses is given by the sum of binomial probabilities for 1, 3, 5... heads. This sum is always 1/2 for any n >= 1.

AI explanation

Using the binomial distribution, the probability of getting an odd number of heads is the sum of probabilities for 1, 3, 5, and so on, heads. This sum equals (1/2) * [ (1/2 + 1/2)^n - (1/2 - 1/2)^n ], which simplifies to 1/2 for any positive integer n. The probability is 1/2.

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