In a standard deck of 52 cards, there are four suits (clubs, hearts, diamonds and spades) and 13 cards of each suit. what is the probability of randomly selecting two cards, which turn out to be the same suit

The probability of randomly selecting two cards which turn out to be the same suit is: 4/17 (0.235)

Step-by-step explanation:

Clubs contain 13 cards, hearts contain 13 cards, diamonds contain 13 cards and spades contain 13 cards as well.

Total number of cards contained in the pack = 52.

Therefore the probability of selecting a card that is a club = 13/52 = 1/4.

The probability of selecting a card that is a heart = 13/52 = 1/4

The probability of selecting a card that is a diamond = 13/52 = 1/4

The probability of selecting a card that is a spade = 13/52 = 1/4

The probability of selecting two cards which turn to be the same suit

= (Probability of selecting two clubs) + (Probability of selecting two hearts) + (Probability of selecting two diamonds) + (Probability of selecting two spades).

Then, probability of selecting two clubs (without replacement)

= (13/52) × (12/51) = 3/51 = 1/17

probability of selecting two hearts (without replacement)

= (13/52) × (12/51) = 3/51 = 1/17

probability of selecting two diamonds (without replacement)

= (13/52) × (12/51) = 3/51 = 1/17

probability of selecting two spades (without replacement)

= (13/52) × (12/51) = 3/51 = 1/17

Since the probability of selecting two cards from the same suit is the addition of the separate probabilities of selecting two clubs, two hearts, two diamonds and two spades, then:

P(two cards from same suit) = (1/17) + (1/17) + (1/17) + (1/17)

= 4/17 (0.235)