Quantitative Literacy Practice Exam 2025 – Comprehensive Preparation Guide

To determine the probability of drawing two aces in a row from a standard deck of 52 playing cards without replacement, we first consider the total number of aces in the deck, which is 4.

When the first ace is drawn, there are 4 aces out of 52 total cards. The probability of drawing an ace first is:

\[ P(\text{first ace}) = \frac{4}{52} \]

After drawing the first ace, there are now 51 cards left in the deck, with 3 aces remaining.

The probability of drawing a second ace after the first ace has already been drawn is:

\[ P(\text{second ace | first ace}) = \frac{3}{51} \]

To find the probability of both events happening (drawing an ace first and then drawing an ace second), we multiply these two probabilities together:

\[

P(\text{two aces}) = P(\text{first ace}) \times P(\text{second ace | first ace})

= \frac{4}{52} \times \frac{3}{51}

\]

This simplifies to:

\[

P(\text{two aces}) = \frac{4 \times