To determine the probability that a card drawn from an ordinary 52-card deck is either a king or a diamond, we can use the principle of inclusion and exclusion. This principle helps us account for cards that might be counted more than once when determining the probability of two events.
1. Total number of cards in the deck:
An ordinary deck contains [tex]\(52\)[/tex] cards.
2. Number of kings in the deck:
There are [tex]\(4\)[/tex] kings in a deck (one in each suit: hearts, diamonds, clubs, and spades).
3. Number of diamond cards in the deck:
There are [tex]\(13\)[/tex] diamond cards in a deck (one for each rank from 2 to 10, Jack, Queen, King, and Ace).
4. Number of cards that are both kings and diamonds:
Since the King of Diamonds is both a king and a diamond, there is [tex]\(1\)[/tex] card that fits both criteria.
To find the probability that the card drawn is either a king or a diamond, we need to find the number of favorable outcomes and divide by the total number of possible outcomes.
First, compute the number of favorable outcomes:
[tex]\[ \text{Favorable outcomes} = (\text{Number of kings}) + (\text{Number of diamonds}) - (\text{Number of cards that are both kings and diamonds}) \][/tex]
[tex]\[ = 4 + 13 - 1 \][/tex]
[tex]\[ = 16 \][/tex]
Now, compute the probability:
[tex]\[ P(\text{King or Diamond}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of cards}} \][/tex]
[tex]\[ = \frac{16}{52} \][/tex]
Convert this fraction to a decimal to match the given multiple-choice options:
[tex]\[ \frac{16}{52} = \frac{4}{13} \approx 0.3077 \][/tex]
Thus, the probability that the card drawn is either a king or a diamond is approximately [tex]\(0.3077\)[/tex], which corresponds to option B.
Hence, the correct answer is:
[tex]\[ \boxed{B. \, P(K \cup D) = 0.31} \][/tex]
