if a coin is tossed 7 times what is the probability that at least one heads and at least one tails shows up

Answer 1

Probability of at least one head = 1 - Prob( no head) = 1 - (1/2)^7 = 1 - 1/128 = 127/128

The same is true for at least one tail, or equivalently 1 - Prob(no tail) = 127/128