Question

a card is drawn from a standard deck of 52 playing cards. find the probability that the card is an ace or a black card.
\\(\frac{15}{26}\\)
\\(\frac{7}{13}\\)
\\(\frac{4}{13}\\)
\\(\frac{29}{52}\\)

Explanation:

Step1: Calculate number of aces

There are 4 aces in a deck, so $n(A)=4$.

Step2: Calculate number of black cards

There are 26 black cards in a deck, so $n(B) = 26$.

Step3: Calculate number of black - aces

There are 2 black - aces, so $n(A\cap B)=2$.

Step4: Use the addition rule of probability

The formula for $P(A\cup B)$ is $P(A\cup B)=\frac{n(A)+n(B)-n(A\cap B)}{n(S)}$, where $n(S) = 52$ (total number of cards). Substitute the values: $\frac{4 + 26-2}{52}=\frac{28}{52}=\frac{7}{13}$.

Answer:

$\frac{7}{13}$