Question

a standard playing card has 52 cards. what is the probability of getting two black cards

Answer 1

To calculate the probability of drawing two black cards from a standard deck of 52 playing cards, we first note that there are 26 black cards (13 spades and 13 clubs) in the deck.

1. **Probability of drawing the first black card**: There are 26 black cards out of 52 total cards. Therefore, the probability of drawing the first black card is:
\[
P(\text{first black}) = \frac{26}{52} = \frac{1}{2}
\]

2. **Probability of drawing the second black card**: After drawing the first black card, there are now 25 black cards left out of a total of 51 remaining cards. Thus, the probability of drawing a second black card is:
\[
P(\text{second black | first black}) = \frac{25}{51}
\]

3. **Finding the combined probability**: To find the probability of both events happening (drawing two black cards in succession), we multiply the probabilities:
\[
P(\text{two black cards}) = P(\text{first black}) \times P(\text{second black | first black}) = \frac{26}{52} \times \frac{25}{51}
\]
Simplifying this:
\[
P(\text{two black cards}) = \frac{1}{2} \times \frac{25}{51} = \frac{25}{102}
\]

Thus, the probability of drawing two black cards from a standard 52-card deck is \(\frac{25}{102}\).