Answer: 1128/5525 = 0.204
There are 52 cards in one deck. First, we list down all the probabilities of picking exactly one ace for each deal:
Getting an ace as the first card:
[tex]\begin{gathered} P(A)=\frac{4}{52} \\ P(C|A)=\frac{48}{51} \\ P(C|CA)=\frac{47}{50} \\ P(ACC)=\frac{376}{5525}\approx0.068 \end{gathered}[/tex]Then, we will find the probability of getting an ace as the second card:
[tex]\begin{gathered} P(C)=\frac{48}{52} \\ P(A|C)=\frac{4}{51} \\ P(C|AC)=\frac{47}{50} \\ P(CAC)=\frac{376}{5525}\approx0.068 \end{gathered}[/tex]Then, the probability of getting an ace on the third card:
[tex]\begin{gathered} P(C)=\frac{48}{52} \\ P(C|C)=\frac{47}{51} \\ P(A|CC)=\frac{4}{50} \\ P(CCA)=\frac{376}{5525}\approx0.068 \end{gathered}[/tex]We will then add all of these probabilities:
[tex]\frac{376}{5525}+\frac{376}{5525}+\frac{376}{5525}=\frac{1128}{5525}\approx0.204[/tex]