A card is drawn from a pack of 52. Find the probability that:
it is an 8 and black in colour.

Answer

To find the probability that a card drawn from a pack of 52 cards is an 8 and black in color, we can follow these steps:

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

### Step 2: Identify the black cards in the deck
In a standard deck, there are two colors of cards: red and black. The black cards consist of:
- Spades
- Clubs

Each of these suits has 13 cards, so the total number of black cards is:
\[ 13 \text{ (Spades)} + 13 \text{ (Clubs)} = 26 \text{ black cards} \]

### Step 3: Identify the number of 8s in the black cards
Among the black cards, we need to find how many are 8s. The black suits (Spades and Clubs) each have one 8:
- 8 of Spades
- 8 of Clubs

Thus, the total number of 8s that are black is:
\[ 1 \text{ (8 of Spades)} + 1 \text{ (8 of Clubs)} = 2 \text{ black 8s} \]

### Step 4: Calculate the probability
The probability \( P \) of drawing an 8 that is black can be calculated using the formula:
\[ P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Here, the number of favorable outcomes (black 8s) is 2, and the total number of outcomes (total cards) is 52.

So, the probability is:
\[ P(\text{8 and black}) = \frac{2}{52} \]

### Step 5: Simplify the fraction
To simplify \( \frac{2}{52} \):
\[ \frac{2}{52} = \frac{1}{26} \]

### Final Answer
The probability that the card drawn is an 8 and black in color is:
\[ \frac{1}{26} \]

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