Question

if you draw one card from a standard deck, what is the probability of drawing a spade or a red card?

Explanation:

Step1: Determine the number of spades and red cards

A standard deck has 52 cards. There are 13 spades. There are 26 red cards (13 hearts + 13 diamonds).

Step2: Use the formula for \(P(A\cup B)\)

The formula for \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Here, \(A\) is the event of drawing a spade and \(B\) is the event of drawing a red card. Since a spade is black, \(P(A\cap B) = 0\).
\(P(A)=\frac{13}{52}\), \(P(B)=\frac{26}{52}\)
\(P(A\cup B)=\frac{13 + 26}{52}=\frac{39}{52}=\frac{3}{4}\)

Answer:

\(\frac{3}{4}\)