The probability of getting exactly k heads in n tosses of a fair coin is given by the binomial distribution formula:
P(k heads in n tosses) = (n choose k) * p^k * (1-p)^(n-k)
where p is the probability of getting a head on any one toss of the coin.
In this case, we want to find the probability of getting 50 heads in 100 tosses of a fair coin, so we have:
P(50 heads in 100 tosses) = (100 choose 50) * 0.5^50 * 0.5^50
= (100 choose 50) * 0.5^100
Using Stirling's approximation for factorials, we can approximate (100 choose 50) as:
(100 choose 50) ≈ (2pi50)^(-1/2) * (100/50)^50
Plugging this into the expression above, we get:
P(50 heads in 100 tosses) ≈ (2pi50)^(-1/2) * (100/50)^50 * 0.5^100
≈ 0.0796
So the closest answer choice is 0.1.