A card is drawn from a standard 52-card deck. What is the probability that the card is a heart or a king?

Solution

Statistics · Medium

Step 1: Identify the two events.

Let H be the event that the card is a heart.
Let K be the event that the card is a king.

There are 13 hearts and 4 kings in a standard deck.

Step 2: Identify the overlap.

The king of hearts belongs to both events.

If we simply add 13 + 4, the king of hearts would be counted twice.

Therefore, subtract the overlap once.

Step 3: Find the number of favorable cards.

13 + 4 - 1 = 16

There are 16 cards that are hearts or kings.

Step 4: Calculate the probability.

P(heart or king) = 16 / 52

Step 5: Simplify the fraction.

16 / 52 = 4 / 13

Therefore, the probability of drawing a heart or a king is 4/13.

Result

4/13