Question

you are dealt one card from a 52 - card deck. find the probability that you are dealt an ace or a black card. click the icon to view a description of a standard deck of playing cards. the probability is (type an integer or a fraction. simplify your answer.)

Explanation:

Step1: Calculate the number of aces, black cards, and black aces

• Number of aces \(n(A)=4\)
• Number of black cards \(n(B) = 26\) (13 spades and 13 clubs)
• Number of black - aces \(n(A\cap B)=2\) (ace of spades and ace of clubs)

Step2: Use the formula for the probability of the union of two events

The formula for \(P(A\cup B)\) is \(P(A\cup B)=\frac{n(A)+n(B)-n(A\cap B)}{n(S)}\), where \(n(S) = 52\) (total number of cards in the deck)

Substitute the values:

$$
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$$

Answer:

\(\frac{7}{13}\)