The king, queen and jack of hearts are removed from a deck of 52 playing cards and well shuffled. One card is selected from the remaining cards. The probability of drawing a '10' of hearts is

Options

A. `(10)/(49)`
B. `(13)/(49)`
C. `(3)/(49)`
D. `(1)/(49)`

Answer

To solve the problem, we will follow these steps:

### Step 1: Determine the total number of cards remaining
Initially, there are 52 cards in a standard deck. We are removing the king, queen, and jack of hearts.

Total cards removed = 3 (king, queen, jack of hearts)

Remaining cards = Total cards - Cards removed
Remaining cards = 52 - 3 = 49

### Step 2: Identify the number of favorable outcomes
We need to find the probability of drawing the '10' of hearts. In a standard deck, there is only one '10' of hearts.

Favorable outcomes = 1 (only one '10' of hearts)

### Step 3: Calculate the probability
Probability (P) is calculated using the formula:
\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Here, the number of favorable outcomes is 1 (the '10' of hearts) and the total number of outcomes is 49 (remaining cards).

Thus, the probability of drawing the '10' of hearts is:
\[ P = \frac{1}{49} \]

### Final Answer
The probability of drawing a '10' of hearts is \( \frac{1}{49} \).

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