Question

select the correct answer from each drop - down menu. trey randomly selects one card a from a standard 52 - card deck. the probability that trey’s card will be a heart or a black - suited card is, because the set of hearts and the set of black - suited cards are sets. the drop - down options for the probability are 1/3, 3/4, 1/39.

Explanation:

Step1: Count favorable card sets

Hearts: 13 cards; black-suited (spades+clubs): 26 cards.

Step2: Calculate total favorable cards

Since hearts and black-suited cards are disjoint (no overlap), total favorable = $13 + 26 = 39$.

Step3: Compute probability

Probability = $\frac{\text{Favorable cards}}{\text{Total deck cards}} = \frac{39}{52} = \frac{3}{4}$.

Step4: Classify set relationship

Hearts (red) and black-suited cards have no common elements, so they are disjoint (mutually exclusive) sets.

Answer:

The probability that Trey's card will be a heart or a black-suited card is $\frac{3}{4}$, because the set of hearts and the set of black-suited cards are disjoint (mutually exclusive) sets.