Question

Assume that the coin is flipped 10 times.
What is the probability that both heads and tails occur?

Answer 1

If you flip 2 coins then 25% chance

Answer 2

P(no heads) = 1/2^10 = 1/1024
P(no tails) = 1/1024
P(no heads|no tails) = 1/1024+1/1024 = 1/512

so, 1-1/512 = 511/512

another way to think of it is that the 1st toss must be identical to the next 9 tosses, so 1/2^9 is the P(next 9 the same)