A standard deck of cards has 52 cards in it. The cards are divided into 4 suits or 13 cards each.If one draws two cards at random from the deck of cards what is the probability that they are of the same suit ?

Question

A standard deck of cards has 52 cards in it. The cards are divided into 4 suits or 13 cards each.If one draws two cards at random from the deck of cards what is the probability that they are of the same suit ?

Answer 1

The first draw is some suit.

The probability that the second draw is that suit is 1/4 = 0.25

Answer 2

number of same suit pairs ... 4 * 13C2

number of pairs ... 52C2

probability ... 4 * 13C2 / 52C2

Answer 3

I assumed you put the first card back. If not then it becomes 12/51

Answer 4

re Damon's answer

after the 1st card is drawn, that suit has fewer cards than the other three suits ... the probability is not 1/4 it is 12/51

but his logic works

Answer 5

so ... replacement or not?

Answer 6

To find the probability that two cards drawn from a standard deck are of the same suit, we need to determine the number of favorable outcomes and the total number of possible outcomes.

Step 1: Find the total number of possible outcomes
In a standard deck of 52 cards, you can select any two cards from it. The order does not matter, so we can use combinations. The total number of possible outcomes is given by the combination formula, "nCr" (read as "n choose r"). In this case, n is 52 (the total number of cards in the deck) and r is 2 (representing the number of cards drawn). The formula for combinations is:
nCr = n! / (r!(n-r)!)

So, the total number of possible outcomes is:
52C2 = 52! / (2!(52-2)!) = (52 * 51) / (2 * 1) = 1326

Step 2: Find the number of favorable outcomes
To calculate the number of favorable outcomes, we need to consider that there are 4 suits, and we want to draw two cards of the same suit.
- For the first card, we have 4 options, as there are 4 suits to choose from.
- For the second card, we need to draw from the same suit as the first card, which leaves us with only 12 cards of the same suit remaining.

So, the number of favorable outcomes is:
4 * 12 = 48

Step 3: Calculate the probability
Finally, we can find the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
P(same suit) = 48 / 1326 = 0.036, or approximately 3.6%

Therefore, the probability that two randomly drawn cards from a standard deck are of the same suit is approximately 3.6%.