Geometric Distribution: 3 Heads.

Question

Tossing a biased coin where $P($Head$)=0.3$, $P($Tail$)=0.7$

I know $P($1st Head Appears After 5 Tosses$)=(0.7)^5$ because first 5 tosses cannot be heads.

What about $P($3rd Head Appears After 5 Tosses$)$?

Answer 1

It is the probability $P(H\leq2)$ where $H$ denotes the number of heads that show up among the first $5$ tosses.

Here $H$ evidently has binomial distribution with parameters $n=5$ and $p=0.3$.