Question

a single card is drawn from a standard 52-card deck. let d be the event that the card drawn is a black card, and let f be the event that the card drawn is a 4 card. find the indicated probability.
p(d∪f)

the probability p(d∪f) is \boxed{}.
(type an integer or a simplified fraction.)

Explanation:

Step1: Define sets

Event D: black cards (26 cards). Event F': non-4 cards (52-4=48 cards). Intersection D∩F': black non-4 cards (26-2=24 cards, since 2 black 4s exist).

Step2: Apply union formula

Use $P(D \cup F') = P(D) + P(F') - P(D \cap F')$. Substitute values:
$P(D)=\frac{26}{52}$, $P(F')=\frac{48}{52}$, $P(D∩F')=\frac{24}{52}$.

Step3: Calculate result

$\frac{26}{52}+\frac{48}{52}-\frac{24}{52}=\frac{26+48-24}{52}=\frac{50}{52}=\frac{25}{26}$.

Answer:

$\frac{25}{26}$