Calculate the probability of getting exactly k heads in n fair coin tosses.
Coin toss probability is a direct application of the binomial distribution. With n independent tosses each having probability p of heads, the probability of exactly k heads is C(n,k) × p^k × (1−p)^(n−k).
P(k heads in n tosses) = C(n,k) × p^k × (1−p)^(n−k)
C(10,5) × 0.5^10 = 252/1024 ≈ 0.2461 or about 24.6%.
For a fair coin, yes. Previous outcomes do not affect future ones — this is the gambler's fallacy.