A standard deck of cards contains 52 cards. Of these cards there are 13 of each type of suit (hearts, spades, clubs, diamonds) and 4 of each type of rank (A – K). Two cards are pulled in order from this deck of 52 playing cards. What is the probability that the cards will be two 10’s?
number of ways to choose 2 of the 4 tens
= C(4,2) = 6
(HS, HC, HD, SC, SD, CD)
number of ways to choose 2 cards from the 52
= C(52,2) = 1326
prob 2 tens = 6/1326 = 1/221
or
prob of first card a ten = 4/52
prob of 2dn card a ten = 3/51
prob 2 tens = (4/52)(3/51) = 12/2652 = 1/221
To find the probability of drawing two 10's from a standard deck of 52 playing cards, we need to determine the number of favorable outcomes (drawing two 10's) and the total number of possible outcomes.
First, let's calculate the number of favorable outcomes. There are 4 cards with the rank of 10 in a deck of 52 cards. So, there are 4 ways to choose the first 10, and once the first 10 is chosen, there are 3 ways to choose the second 10 (since we can't choose the same card twice). This gives us a total of 4 x 3 = 12 favorable outcomes.
Next, let's determine the total number of possible outcomes. When we draw the first card, there are 52 cards to choose from. Once the first card is drawn, there are 51 cards remaining for the second draw. So, the total number of possible outcomes is 52 x 51 = 2,652.
Now, 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
Probability = 12 / 2652
Reducing the fraction to its simplest form, we get:
Probability = 1 / 221
Therefore, the probability of drawing two 10's from a standard deck of 52 playing cards is 1 in 221.