One card is selected at random from a deck of cards. Determine the probability of selecting a card that is less than 8 or a heart. Note that the ace is considered a low card.
The probability that the card selected is less than 8 or a heart is
(Type an integer or a simplified fraction.)

To find the probability of selecting a card that is less than 8 or a heart, let’s start by calculating the individual probabilities. There are 7 cards (Ace through 7) that are considered less than 8 in each suit, giving a total of 28 cards (7 cards x 4 suits). Next, there are 13 hearts in the deck. However, we must be careful not to double-count the hearts that are less than 8 (Ace, 2, 3, 4, 5, 6, 7), which add up to 7 cards.

So, using the principle of inclusion-exclusion:

Applying the formula:
Probability (less than 8 or heart) = P(less than 8) + P(heart) - P(both)
= (28/52) + (13/52) - (7/52)
= (34/52)

Simplifying gives us:
= 17/26

Therefore, the probability that the card selected is less than 8 or a heart is 17/26.