Final answer:
The probability that Trey's card will be a heart or a black-suited card is 3/4.
Step-by-step explanation:
To find the probability that Trey's card will be a heart or a black-suited card, we need to calculate the probability of each event and add them together.
- Probability of selecting a heart: There are 13 hearts in a standard deck of 52 cards, so the probability is 13/52, or 1/4.
- Probability of selecting a black-suited card: There are 26 black-suited cards (clubs and spades) in a deck of 52 cards, so the probability is 26/52, or 1/2.
To find the probability of both events happening, we can add the probabilities together: 1/4 + 1/2 = 3/4.
Therefore, the probability that Trey's card will be a heart or a black-suited card is 3/4.