Question 46·Easy·Probability and Conditional Probability
A single card is randomly selected from a standard deck of 52 playing cards. What is the probability that the card selected is a heart?
For card probability questions on the SAT, first recall the basic deck facts: 52 cards total, 4 suits, 13 cards per suit, and 26 red/26 black. Then quickly identify the number of favorable outcomes (how many cards match the condition) and put that over 52. Finally, simplify the fraction. Be careful not to confuse suits (4 types), colors (2 types), and ranks (13 types), since each leads to different probabilities.
Hints
Recall how a standard deck is organized
Think about how many total cards are in a standard deck and how they are grouped into suits (hearts, diamonds, clubs, spades).
Find the number of hearts
Hearts are one of the suits. If the 52 cards are split evenly among the 4 suits, how many cards are in each suit, and therefore how many are hearts?
Use the basic probability formula
Probability is . Use your count of heart cards over 52, then simplify the fraction.
Desmos Guide
Use Desmos to confirm the fraction
In Desmos, type 13/52 on a new line. Look at the simplified fraction (and decimal, if shown) that Desmos gives you; that simplified fraction is the probability of drawing a heart.
Step-by-step Explanation
Understand the structure of a standard deck
A standard deck of playing cards has 52 cards in total.
These 52 cards are divided into 4 suits:
- Hearts
- Diamonds
- Clubs
- Spades
Because the deck is evenly divided, each suit has the same number of cards.
Count favorable outcomes and total outcomes
Each suit has 13 cards.
- Number of heart cards (favorable outcomes) = 13
- Total number of cards in the deck (total outcomes) = 52
For probability, we use the formula:
So for drawing a heart, the probability is before simplifying.
Compute and simplify the probability
We found that the probability of drawing a heart is .
Now simplify by dividing the numerator and denominator by their greatest common divisor, which is 13:
So, the probability that the card selected is a heart is .