Question

find the probability that a person tossing 8 coins will get either all heads or all tails for the first time on the seventh toss?

Answer 1

Probability of getting 8 heads (tails) in one toss: $(\frac{1}{2})^8=\frac{1}{256}$

Probability of getting 8 heads or tails in one toss: $\frac{1}{256}*2=\frac{1}{128}$

Probability of getting 8 heads or tails for the first time on seventh toss: $(1-\frac{1}{128})^6*\frac{1}{128}=\frac{127^6}{128^7}\approx 2.26*10^{-13}$