Question

if two cards are drawn without replacement from a standard 52 - card deck, find the probability that the second card is an ace, given that the first card was an ace.

a. \\( \frac { 4 } { 51 } \\)
b. \\( \frac { 3 } { 52 } \\)
c. \\( \frac { 3 } { 51 } \\)
d. \\( \frac { 1 } { 3 } \\)

Explanation:

Step1: Determine the remaining number of aces

A standard deck has 4 aces. After drawing one ace, there are \(4 - 1=3\) aces left.

Step2: Determine the remaining number of cards

Originally, there are 52 cards. After drawing one card (an ace), there are \(52 - 1 = 51\) cards left.

Step3: Calculate the probability

The probability that the second card is an ace, given the first was an ace, is the number of remaining aces divided by the number of remaining cards. So the probability \(P=\frac{3}{51}\).

Answer:

C. \(\frac{3}{51}\)