While shuffling a pack of 52 playing cards, 2 are accidentally dropped. Find the probability that the missing cards to be of different colours.

Options

A. `(29)/(52)`
B. `(1)/(2)`
C. `(26)/(51)`
D. `(27)/(51)`

Explanation

To solve the problem of finding the probability that the two missing cards from a shuffled pack of 52 playing cards are of different colors, we can follow these steps:

### Step 1: Understand the Composition of the Deck
A standard deck of 52 playing cards consists of:
- 26 red cards (hearts and diamonds)
- 26 black cards (clubs and spades)

### Step 2: Total Ways to Choose 2 Cards
The total number of ways to choose any 2 cards from the 52 cards is given by the combination formula:
\[ \text{Total ways} = \binom{52}{2} = \frac{52 \times 51}{2} = 1326 \]

### Step 3: Calculate the Favorable Outcomes
To find the probability that the two missing cards are of different colors, we need to calculate the number of ways to choose one red card and one black card.

- The number of ways to choose 1 red card from 26 red cards is:
\[ \binom{26}{1} = 26 \]

- The number of ways to choose 1 black card from 26 black cards is:
\[ \binom{26}{1} = 26 \]

- Therefore, the total number of ways to choose 1 red card and 1 black card is:
\[ \text{Favorable outcomes} = 26 \times 26 = 676 \]

### Step 4: Calculate the Probability
Now, we can find the probability that the two missing cards are of different colors:
\[ \text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total ways}} = \frac{676}{1326} \]

### Step 5: Simplify the Probability
We can simplify the fraction:
\[ \frac{676}{1326} = \frac{26}{51} \]

Thus, the probability that the two missing cards are of different colors is:
\[ \boxed{\frac{26}{51}} \]