Question

what is the probability of getting either a diamond or a king when drawing a single card from a deck of 52 cards? the probability that the card is either a diamond or a king is (simplify your answer. type a fraction.)

Explanation:

Step1: Calculate the number of diamond cards and king cards

There are 13 diamond cards in a deck. There are 4 king cards in a deck. But the king of diamonds is counted in both groups. So the number of cards that are either a diamond or a king is \(13 + 4-1=16\) (using the formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\), where \(A\) is the set of diamond cards and \(B\) is the set of king cards, and \(n(A\cap B) = 1\) (the king of diamonds)).

Step2: Calculate the probability

The probability \(P\) of an event is given by \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the total number of outcomes is 52 (since there are 52 cards in a deck), and the number of favorable outcomes is 16. So \(P=\frac{16}{52}\).

Step3: Simplify the fraction

Simplify \(\frac{16}{52}\) by dividing both the numerator and the denominator by 4. \(\frac{16\div4}{52\div4}=\frac{4}{13}\).

Answer:

\(\frac{4}{13}\)