Question

A standard deck of 52 cards contains four suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. Two cards are randomly drawn without replacement. Calculate the probability of drawing two diamond cards. Express your answer in percent form rounding to the nearest hundredth.(1 point

Answer 1

is the bot correct?

Answer 2

@cheesecrackers he has 6 upvotes, so I think so

Answer 3

First, we need to find the total number of ways to draw 2 cards from a deck of 52 cards, without replacement. This can be calculated using the combination formula:

C(n, r) = n! / (r!(n-r)!)

Where n is the total number of cards in the deck (52) and r is the number of cards being drawn (2):

C(52, 2) = 52! / (2!(52-2)!) = (52*51) / (2*1) = 1326

Next, we need to find the number of ways to draw 2 diamond cards. There are 13 diamond cards in a deck, so the number of ways to draw 2 diamond cards can be calculated as:

C(13, 2) = 13! / (2!(13-2)!) = (13*12) / (2*1) = 78

Finally, we calculate the probability of drawing two diamond cards by dividing the number of ways to draw 2 diamond cards by the total number of ways to draw 2 cards:

Probability = 78 / 1326 ≈ 0.0588

Converting this to a percentage rounded to two decimal places, we get:

Probability in percent form ≈ 5.88%