A coin is tossed 3 times. If the same side falls for all of the three times, the coin gets tossed once more. Describe the space of elementary events and find the CDF of the vector $(X, Y)$, where $X$ is the number of fallen tails and $Y$ is the number of tosses.
I have tried calculating the probabilities for $X=0, Y=0$, $X=1, Y=0$, and so on.. but haven't gotten the right result. Hints on how to approach this problem would be great, thanks.