​Two cards are drawn from a pack of 52 cards. The probability that out of 2 cards, one card is red and one card is black is:

Correct option is C

​

Given:

Total number of cards in a standard deck = 52

Number of red cards in the deck = 26 (hearts + diamonds)

Number of black cards in the deck = 26 (clubs + spades)

Formula Used:

The probability of an event is given by:
P(E) =  $$\frac{(Number \ of \ favorable \ outcomes) }{(Total \ number \ of \ outcomes)}$$​​

Step-by-Step Calculation:

Total number of ways to choose 2 cards from 52 cards:
The total number of ways to draw 2 cards from a deck of 52 cards is given by:
C(52, 2) =  $$\frac{(52 × 51) }{2} = 1326$$​​

Number of favorable outcomes (one red card and one black card):
To get one red card and one black card, we select:
- 1 red card out of 26 red cards: C(26, 1) = 26
- 1 black card out of 26 black cards: C(26, 1) = 26
Thus, the total number of favorable outcomes is:
26 × 26 = 676

Probability:
The probability of getting one red card and one black card is:
P(E) = (Number of favorable outcomes) / (Total number of outcomes)
P(E) =  $$\frac{676 }{ 1326}$$​​
Simplifying the fraction:
P(E) =  $$\frac{26 }{51}$$​​