If you toss a fair coin four times, the probability of any specific outcome is the same. Consider the following example:
Event A: Heads, Tails, Heads, Tails
Event B: Heads, Heads, Heads, Heads
P(A) = P(B) = 0.5^4 = 6.25%
However, the chance of having any Tails in the sequence is : P(Any Tails) = 1 - P(B) = 1 - 0.0625 = 93.75%
If we tossed a fair coin 100 times, then P(Any Tails) would be very close to 1, which makes me think that a sequence that has only heads is less likely to happen than any sequence that has at least one tails.
Should the probability of P(Any Tails) affect the probability of P(B)? If yes, how should it be computed? Otherwise, why is my intuition wrong ?