Here's a problem and I have a small doubt.
We flip a coin. We get a head with probability 0.2 on each flip. Each flip is independent. If the player wins (head), he stops. If he loses, he plays again.
What is the probability of the event H: win in less than 3 flips ?
I know that I can answer the following way:
Let G: Getting at least 3 tails.
$P(H)=1 - P(G)=1 - 0,8*0,8*0,8 = 0,488$ which is the right answer.
BUT, we could also say: $P(H) = P(H_1) + P(T_1H_2) = 0,2 + 0,8*0,2 = 0,36$ ?????????
Why is my second result different from the first one please?
Can anyone help ?