Three cards of spades are lost from a pack of 52 playing cards. The remaining cards were well shuffled and then a card was drawn at random from them. Find the probability that the drawn card is of black colour.

Options

A. `(26)/(49)`
B. `(23)/(49)`
C. `(13)/(26)`
D. `(23)/(52)`

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Determine the total number of cards remaining
Initially, there are 52 cards in a standard deck. If 3 cards of spades (which are black cards) are lost, we need to subtract these from the total.

**Calculation:**
Total cards remaining = 52 - 3 = 49

### Step 2: Determine the number of black cards remaining
In a standard deck, there are 26 black cards (13 spades and 13 clubs). Since 3 spade cards are lost, we need to adjust the number of black cards accordingly.

**Calculation:**
Remaining black cards = 26 - 3 = 23

### Step 3: Calculate the probability of drawing a black card
The probability of an event is given by the formula:

\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

In this case, the number of favorable outcomes (drawing a black card) is 23, and the total number of outcomes (total cards remaining) is 49.

**Calculation:**
\[ \text{Probability of drawing a black card} = \frac{23}{49} \]

### Final Answer
The probability that the drawn card is of black color is \(\frac{23}{49}\).

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