Question

in a standard deck of cards, what is the probability of picking a queen of a diamond or a red card

Explanation:

Step1: Determine the number of red cards and the queen of diamonds

A standard deck has 52 cards. There are 26 red cards (13 hearts and 13 diamonds). The queen of diamonds is 1 card. But since the queen of diamonds is already a red card, we don't double - count it.

Step2: Use the formula for probability

The formula for probability \(P(A)=\frac{n(A)}{n(S)}\), where \(n(A)\) is the number of favorable outcomes and \(n(S)\) is the total number of outcomes. Here, \(n(A) = 26\) (red cards, and the queen of diamonds is already included in the red cards), \(n(S)=52\)

$$P=\frac{26}{52}$$

Answer:

\(\frac{1}{2}\)