A card drawn at random is a probability question: count the cards that match the target, then divide by all the cards that could be drawn. A standard deck has four equally sized suits, so you can find the heart count from the deck total. Keep the entire deck in the denominator; using only red cards changes the group being sampled.
Hints
- Hint 1
A suit is a card category, such as hearts or spades. The four suits have equal numbers of cards. How many of the cards belong to each suit?
- Hint 2
For probability, put the number of cards that match the target over the number that could be picked. The card comes from the whole deck, so what belongs in the denominator?
Step-by-step
Count hearts, then compare with the deck
Step 1Count the hearts
No Desmos needed. A standard deck has four equally sized suits. The four suits, or card categories, are hearts, diamonds, clubs, and spades. Divide the cards among them to find the heart count:
- Step 2
Set up the probability
A favorable outcome is a card that matches the target, so there are favorable cards. Put matching cards over all cards that could be picked. The card is selected from the full -card deck, not just the red cards, so
- Step 3
Reduce the fraction
Divide the numerator (top) and denominator (bottom) by :
So the probability of selecting a heart is . Choice D.