Answer:
Probability is: [tex]$ \frac{\textbf{13}}{\textbf{51}} $[/tex]
Step-by-step explanation:
From a deck of 52 cards there are 26 black cards. (Spades and Clubs).
Also, there are 26 red cards. (Hearts and Diamonds).
First, we determine the probability of drawing a black card.
P(drawing a black card) = [tex]$ \frac{number \hspace{1mm} of \hspace{1mm} black \hspace{1mm} cards}{total \hspace{1mm} number \hspace{1mm} of \hspace{1mm} cards} $[/tex] [tex]$ = \frac{26}{52} = \frac{\textbf{1}}{\textbf{2}} $[/tex]
Now, since we don't replace the drawn card, there are only 51 cards.
But the number of red cards is still 26,
∴ P(drawing a red card) = [tex]$ \frac{number \hspace{1mm} of \hspace{1mm} red \hspace{1mm} cards}{total \hspace{1mm} number \hspace{1mm}of \hspace{1mm} cards} $[/tex] [tex]$ = \frac{26}{51} $[/tex]
Now, the probability of both black and red card = [tex]$ \frac{1}{2} \times \frac{26}{51} $[/tex]
[tex]$ = \frac{\textbf{13}}{\textbf{51}} $[/tex]
Hence, the answer.
