I have the following problem : We have 2/3 of getting heads when we throw a coin. We have 1/3 of getting tails when we throw a coin.
What is the probability of getting exactly two heads after three throws knowing that the first throw was a head.
My probability knowledge is a little bit rusty. I know that this looks like a conditional probability problem. I know that the formula for conditional probability is $P(X|Y) = \dfrac{P(X \cap Y)}{P(Y)}$.
Now I need to adapt this formula to our current problem. Initially we had a probability of $\dfrac{2}{3}$ of getting a heads. Wait... It seems that it does not matter what was the result at the first throw because the probability of getting a heads is still 2/3 at each throws it seems. Now I'm confused. Could someone help me clear this confusion? What should I do?