Question

You have 52 cards and you choose 2 what is probability of drawing 2 cards of the same suite

Answer 1

In a pack of 52 cards, there are 26 black cards (13 spade and 13 club), and 26 red cards (13 heart and 13 diamond).

Now, the probability of selecting 1st card from 52 cards: 1;

Remaining cards of same colors = 25;
And, Total remaining cards = 51; 

So, the probability of selecting 2nd card of same color = (1 x 25) / 51
                                                                                       = 25/51

An Alternate Method:

The probability of getting two red cards is 26/52 x 25/51
   = 1/2 x 25/51
   = 25/102.

Since the number of black cards is the same as the number of reds, the probability of selecting two black cards is also 25/102.

So, the probability of selecting two cards of the same color (either both red or both black) is 25/102 + 25/102 = 25/51.

By using PnC:

Total ways = 52C2

Selecting both Red cards = 26C2

Selecting both Black cards = 26C2

Thus, Probability = (2 x 26C2)/52C2
                            = 25/51

∴ The probability of drawing 2 cards of the same suite is 25/51


Regards

#Exotic Explorer