Answer: 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)
