Answer
P(ace or heart) $=\frac{4}{13}\approx0.308$
Work Step by Step
The sample space S = "a standard 52-card deck". So, N(S) = 52.
Let E be the event "an ace card". So, as shown in Figure 9, N(E) = 4.
Let H be the event "a diamond card". So, as shown in Figure 9, N(H) = 13
The events "an ace card" and "a heart card" are not mutually exclusive. There is one outcome in common, the ace of hearts, which means N(ace and heart) = 1. Now, using The General Addition Rule:
P(ace or heart) = P(ace) + P(heart) - P(ace and heart) =
$\frac{N(ace)}{N(S)}+\frac{N(heart)}{N(S)}-\frac{N(\text{ace and heart})}{N(S)}=\frac{4}{52}+\frac{13}{52}-\frac{1}{52}=\frac{16}{52}=\frac{4}{13}\approx0.308$
