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

$\frac{1}{2}$

The correct answer is Option (2) → $\frac{1}{2}$

Let n = 100 tosses of a fair coin.

Probability of getting head an odd number of times in n tosses of a fair coin:

For a fair coin, P(head) = P(tail) = 1/2

Sum of probabilities of odd number of heads =$ 1/2 (1 - (1 - 1)^n/2^n) = 1/2$

More formally:

For a fair coin, the probability of odd number of heads in n tosses is 1/2 if n is even.

Here, n = 100 (even) ⇒ Probability = 1/2