Question

compound probabilities-mutually exclusive events

a card is drawn from a standard 52-card deck. there are 13 hearts and 13 diamonds in the deck. what is the probability of drawing a heart or diamond?

\\(p(\text{heart or diamond}) = \quad\\%\\)

round your answer to the nearest whole percent.

Explanation:

Identify the given values and target

Given:

• Total cards in a standard deck: \(N = 52\)
• Number of hearts: \(N(\text{Heart}) = 13\)
• Number of diamonds: \(N(\text{Diamond}) = 13\)

Target:

• \(P(\text{Heart or Diamond})\) as a percentage rounded to the nearest whole percent.

Apply mutually exclusive probability formula

Since a card cannot be both a heart and a diamond, these are mutually exclusive events:

$$ P(\text{Heart or Diamond}) = P(\text{Heart}) + P(\text{Diamond}) $$

$$ P(\text{Heart or Diamond}) = \frac{13}{52} + \frac{13}{52} = \frac{26}{52} = \frac{1}{2} $$

Convert to percentage

$$ \frac{1}{2} = 0.5 = 50\% $$

Answer:

A card is drawn from a standard 52-card deck. There are 13 hearts and 13 diamonds in the deck. What is the probability of drawing a heart or diamond?

\(P(\text{Heart or Diamond}) =\) <blank>50</blank>%