Question

in a standard deck of cards, what is the probability of picking a spade or king.

Explanation:

Step1: Find number of spades and kings

A standard deck has \(52\) cards. There are \(13\) spades (\(n(S)=13\)). There are \(4\) kings (\(n(K) = 4\)). But the king of spades is counted twice. So \(n(S\cap K)=1\).
Using the formula \(n(S\cup K)=n(S)+n(K)-n(S\cap K)\), we get \(n(S\cup K)=13 + 4-1=16\).

Step2: Calculate probability

Probability \(P=\frac{n(S\cup K)}{n(\text{total cards})}\). Since \(n(\text{total cards}) = 52\), \(P=\frac{16}{52}=\frac{4}{13}\).

Answer:

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