Question

1. a card is drawn from an ordinary deck of cards. what is the probability of drawing a number card (not including the ace) or a king?

a. \\(\frac{4}{13}\\)

b. \\(\frac{1}{52}\\)

c. \\(\frac{13}{52}\\)

d. \\(\frac{10}{13}\\)

Explanation:

⚡ Using what you learned: Simple Events and Compound Events

Step 1: Identify the total number of outcomes

An ordinary deck of cards has a total of 52 cards:

$$ N = 52 $$

Step 2: Count the favorable outcomes

We want to find the probability of drawing a number card (excluding the ace) OR a king.

• Number cards (excluding Ace): These are the cards numbered 2 through 10. There are 9 such ranks (2, 3, 4, 5, 6, 7, 8, 9, 10). Since there are 4 suits, the number of these cards is:

$$ 9 \times 4 = 36 $$

• Kings: There are 4 kings in a deck (one for each suit):

$$ 4 $$

Since a card cannot be both a number card and a king, these events are mutually exclusive. The total number of favorable cards is:

$$ 36 + 4 = 40 $$

Step 3: Calculate the probability

The probability \( P \) is the ratio of favorable outcomes to total outcomes:

$$ P = \frac{40}{52} $$

Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 4:

$$ P = \frac{40 \div 4}{52 \div 4} = \frac{10}{13} $$

Answer:

D. \(\frac{10}{13}\)