Given a shuffled poker deck, if we draw one card at a time from the top and stop when we draw an ace, and denote $X$ as the number of cards we have drawn, what is $P(X=10)$?
I am thinking $P(\text{ace})$, which is $\frac{18472}{54145}$ but the system does not accept it.
Can someone please help me understand the questions even?
You have to draw nine non-aces followed by an ace. The chance the first card is not an ace is $\frac {48}{52}$. Assuming it is not an ace, the chance the second card is not an ace is $\frac {47}{51}$ and so on. After nine non-aces, the chance of an ace is $\frac 4{43}$. Multiply them all together and you are there.