Question

For this problem, we're going to use a regular deck of playing cards. The order that you select the cards does not matter. (don't use commas in your answers)

We're going to pick 2 cards from a deck of cards.
How many items are in the sample space?
There are 12 face cards in a deck of playing cards.
How many ways can we select 2 face cards?
What is the probability that we selected 2 face cards when we picked our two cards? (Write your answer as numerator/denominator)

Answer 1

There are 1,326 possible outcomes when selecting 2 cards from a deck. There are 66 ways to select 2 face cards from the 12 face cards available. The probability of selecting 2 face cards is 1/20.

Step-by-step explanation:

To determine the sample space, we calculate the total number of ways to select 2 cards from a deck of 52 cards. This can be done using combinations since the order of selection does not matter, which is calculated as C(n, k) = n! / (k!(n-k)!).

For the entire deck, the sample space consists of C(52, 2) = 52! / (2!(52-2)!) = 1,326 possible outcomes.

To find out how many ways we can select 2 face cards from the 12 available, we calculate C(12, 2) = 12! / (2!(12-2)!) = 66 ways.

The probability of selecting 2 face cards is given by dividing the number of favorable outcomes by the number of possible outcomes in the sample space. Thus, the probability is P(2 face cards) = 66 / 1,326, which simplifies to 1/20.