Question

A single card is to be drawn from a 52-card deck.(the sample space S has 52 elements.) Find each of the following, given the events. A: the selected card is a face card. B: the selected card is black.

Answer 1

The first thing to know is that the probability of drawing any card is

$P=\frac{1}{52}$

Now within a deck of 52 cards we have 12 figures in total. Also the deck can be either black or red.

A) So for the first part the probability that from a deck of 52 cards you will draw a face card is:

$\begin{gathered} P_A=\frac{12}{52} \\ P_A=0.23 \end{gathered}$

B) And if we want to know if the letter that we will draw is only black:

$\begin{gathered} P_B=\frac{26}{52} \\ P_B=0.5 \end{gathered}$

C) If we want to know what is the probability that we will draw from a deck a card that is face card and black, we have to know how many cards are black of the 12 that are face card, as we only have 2 options or red or black the number of black figure cards are 6

$\begin{gathered} P_{\text{A}\cap\text{B}}=P_A\cdot P_B \\ P_{\text{A}\cap\text{B}}=0.23\cdot0.5 \\ P_{\text{A}\cap\text{B}}=0.11 \end{gathered}$