Ramesh draws a card randomly from a deck of 52 cards. The probability that this card bears an even number in black is:

Options

A. `(1)/(13)`
B. `(1)/(52)`
C. `(2)/(13)`
D. `(5)/(26)`

Answer

To find the probability that Ramesh draws a card that bears an even number in black from a standard deck of 52 cards, we can follow these steps:

### Step 1: Identify the total number of cards in the deck.
A standard deck of cards contains 52 cards.

**Hint:** Remember that a standard deck has 4 suits: hearts, diamonds, clubs, and spades.

### Step 2: Identify the black suits.
The black suits in a deck of cards are clubs and spades.

**Hint:** There are 2 black suits in a deck.

### Step 3: Identify the even numbers in the black suits.
The even numbers in a deck of cards are 2, 4, 6, 8, and 10. Each black suit (clubs and spades) has these even numbers.

**Hint:** Count the even numbers available in one black suit and remember that there are two black suits.

### Step 4: Calculate the total number of even black cards.
Each black suit has 5 even cards (2, 4, 6, 8, 10). Therefore, in both black suits, the total number of even cards is:
\[ 5 \text{ (from clubs)} + 5 \text{ (from spades)} = 10 \text{ even black cards} \]

**Hint:** Multiply the number of even cards in one suit by the number of black suits.

### Step 5: Calculate the probability.
The probability \( P \) of drawing an even number in black is given by the formula:
\[ P(\text{even black}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values:
\[ P(\text{even black}) = \frac{10}{52} \]

### Step 6: Simplify the probability.
To simplify \( \frac{10}{52} \):
\[ \frac{10}{52} = \frac{5}{26} \]

**Hint:** Always simplify fractions to their lowest terms.

### Final Answer:
The probability that Ramesh draws a card that bears an even number in black is \( \frac{5}{26} \).