Multiple choice

A fair coin is tossed $100$ times. The probability of getting tails an odd number of times is

  1. $\dfrac {1}{2}$
  2. $\dfrac {1}{4}$
  3. $\dfrac {1}{8}$
  4. $\dfrac {3}{8}$
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A Correct answer
Explanation

For any number of tosses n, the probability of getting an odd number of tails is exactly 1/2, because the binomial expansion of (p+q)^n and (p-q)^n leads to the sum of odd terms being equal to the sum of even terms when p=q=1/2.

AI explanation

For a fair coin tossed n times, the sum of the probabilities of getting an even number of tails and an odd number of tails is 1. Because the coin is fair, these probabilities are perfectly symmetrical, meaning the probability of getting an odd number of tails equals the probability of getting an even number of tails. Therefore, the probability of getting an odd number of tails in 100 tosses is exactly 1/2.

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