Question

2 cards are chosen from a deck of cards. The first card is replaced before choosing the second card. What is the probability that theyboth will be face cards?

Answer 1

Explanation

Given: A deck of cards

We are required to determine the probability that the two chosen cards are face cards.

This is achieved thus:

We know that the face cards in a deck of cards are the Kings, Queens, and Jacks.

We also know that a deck of 52 cards can be broken down thus:

The probability of an event is given as:

$P=\frac{Number\text{ }of\text{ }required\text{ }outcome}{Number\text{ }of\text{ }total\text{ }outcome}=\frac{n(E)}{n(S)}$

Therefore, we have:

$\begin{gathered} n(E)=12 \\ n(S)=52 \\ P(Face\text{ }cards)=\frac{12}{52}\times\frac{12}{52} \\ =\frac{3}{13}\times\frac{3}{13} \\ =\frac{9}{169} \end{gathered}$

Hence, the answer is:

$\frac{9}{169}$