Sure, let's solve this problem step-by-step.
We're tasked with finding the probability of drawing either a number card or a king from a standard deck of 52 cards.
1. Identify the total number of cards: In a standard deck, there are 52 cards.
2. Identify the number of number cards: Number cards refer to cards numbered from 2 to 10. There are 9 number cards in each suit (2 through 10).
Since there are 4 suits (hearts, diamonds, clubs, and spades), the total number of number cards in the deck is:
[tex]\[
9 \text{ cards/suit} \times 4 \text{ suits} = 36 \text{ number cards}
\][/tex]
3. Identify the number of kings: There are 4 kings in a deck, one in each suit.
4. Find the total number of favorable outcomes: This is the sum of the number cards and the kings.
[tex]\[
36 \text{ number cards} + 4 \text{ kings} = 40 \text{ favorable outcomes}
\][/tex]
5. Calculate the probability: Probability is given by the ratio of the number of favorable outcomes to the total number of possible outcomes (total cards in the deck).
[tex]\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{40}{52}
\][/tex]
6. Simplify the fraction:
[tex]\[
\frac{40}{52} = \frac{10}{13}
\][/tex]
Therefore, the probability of drawing a number card or a king from a standard deck of cards is [tex]\(\frac{10}{13}\)[/tex].
The correct answer is:
[tex]\[
\boxed{\frac{10}{13}}
\][/tex]
