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