36. Find the probability of drawing a number card or a king from a standard deck of cards.

A. [tex]$\frac{10}{13}$[/tex]

B. [tex]$\frac{1}{2}$[/tex]

C. [tex]$\frac{4}{13}$[/tex]

D. [tex]$\frac{3}{4}$[/tex]



Answer :

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]