Final answer:
The probability that two cards drawn from a standard deck of 52 cards have the same suit is 12/51 or about 23.53%.
Step-by-step explanation:
The question involves calculating the probability of drawing two cards from a standard 52-card deck and both cards having the same suit. The probability calculation is based on the principles of combinatorics and probability theory, which is a part of high school mathematics curriculum.
To find the probability that two cards drawn from a 52-card deck have the same suit, we need to consider that there are four suits (clubs, diamonds, hearts, and spades) and 13 cards in each suit. When the first card is drawn, there is no condition to meet, but after drawing the first card of any suit, there are now 12 cards left of that suit out of the remaining 51 cards.
The probability of the second card matching the suit of the first card is therefore 12/51. This is because there are 12 favorable outcomes (remaining cards of the same suit) out of 51 possible outcomes (total remaining cards).
Probability calculation
:
- Draw the first card; there are no restrictions so it can be any card from the 52-card deck.
- Draw the second card; it has to be of the same suit as the first card. There are now 12 cards that match the suit of the first card out of 51 cards left.
The formula for probability is the number of favorable outcomes divided by the number of possible outcomes, which gives us:
P(same suit) = 12/51 ≈ 0.2353
So, the probability of drawing two cards from a standard deck and having them be of the same suit is roughly 23.53%.