Answer
F or G = {5, 6, 7, 8, 9, 10, 11, 12}
$P(F or G) = \frac{8}{12}\approx0.667$
$P(F or G)=P(F)+P(G)-P(F and G)=\frac{5}{12}+\frac{4}{12}-\frac{1}{12}=\frac{8}{12}\approx0.667$
Work Step by Step
S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. So, $N(S)=12$.
F = {5, 6, 7, 8, 9}. So, $N(F)=5$.
G = {9, 10, 11, 12}. So, $N(G)=4$.
F or G = {5, 6, 7, 8, 9, 10, 11, 12}. So, $N(F or G)=8$.
F and G = {9}. So, $N(F and G)=1$
By counting:
$P(F or G)=\frac{N(F or G)}{N(S)}=\frac{8}{12}\approx0.667$.
Using the General Addition Rule:
$P(F or G)=P(F)+P(G)-P(F and G)=\frac{N(F)}{N(S)}+\frac{N(G)}{N(S)}-\frac{N(F and G)}{N(S)}=\frac{5}{12}+\frac{4}{12}-\frac{1}{12}=\frac{8}{12}\approx0.667$.
