Waiting More Than Five Flips

More than five flips are required exactly when the first five flips are all tails.

Multiply the probability of five consecutive tails.

1. 1. Translate the event

   Needing more than five flips means the first five flips are all tails.

   $$P(T>5)=P(\text{first 5 flips all tails})$$

2. 2. Compute the probability

   Each flip is tails with probability $1/2$, independently.

   $$P={\left(\frac{1}{2}\right)}^5=\frac{1}{32}$$

Answer: 1/32