Question

Two cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected . Find the probability of selecting a black card and selecting a red card. The probability of selecting a black card and then selecting a red card is

Answer 1

Answer:

Probability is:   $\frac{\textbf{13}}{\textbf{51}}$

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) = $\frac{number \hspace{1mm} of \hspace{1mm} black \hspace{1mm} cards}{total \hspace{1mm} number \hspace{1mm} of \hspace{1mm} cards}$  $= \frac{26}{52} = \frac{\textbf{1}}{\textbf{2}}$

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) = $\frac{number \hspace{1mm} of \hspace{1mm} red \hspace{1mm} cards}{total \hspace{1mm} number \hspace{1mm}of \hspace{1mm} cards}$  $= \frac{26}{51}$

Now, the probability of both black and red card = $\frac{1}{2} \times \frac{26}{51}$

$= \frac{\textbf{13}}{\textbf{51}}$

Hence, the answer.