First Head on Flip Four

The first three flips must be tails, and the fourth flip must be heads.

Multiply the probability of each of these four independent events.

1. 1. Set up the geometric probability

   The first head on flip $4$ requires three tails followed by a head.

   $$P(T=4)=(1-p{)}^{3}p$$

2. 2. Substitute the value

   With $p=0.3$, compute the product.

   $$P=(0.7{)}^3(0.3)=0.1029$$

Answer: 0.1029