There are 52 cards in a standard deck of cards.
In each deck of cards, there are 4 "suits."
These are the diamonds, hearts, spades, and clubs.
Each suit contains 13 cards.
This means that there is a 13 in 52 chance of picking a card from each suit.
13/52 chance of diamonds, 13/52 chance of hearts, 13/52 chance of spades, 13/52 chance of clubs.
The probability of first picking a card from the spades suit is 13/52.
This can simplify to 1/4 by dividing each side of the fraction by 13.
13 ÷ 13 = 1
52 ÷ 13 = 4
So the probability of picking one card and it being a spade is 1/4.
The probability of picking a card from the diamonds suit is the same, since each suit has the same amount of cards.
So the probability of picking a card and it being a diamond is 13/52, or 1/4 as well.
However, to find the probability that both of these events will happen, we have to do something different.
The first probability (spade) is 1/4.
If you don't place this card back and then draw another, there is are only 51 cards in the deck, but still 13 diamonds cards.
So, after picking a spades card (1/4 probability), there is a 13/51 chance you will pick a card from the diamonds suit.
To find this compound probability, multiply both of these singular probabilities together.
1/4 • 13/51
= 13/204
This is in simplest form.
The probability of selecting a spade, not placing it back into the deck, and then drawing a diamond is 13/204.
The answer to this question is 13/204.
Hope this helps!
