Question

After growing tired of squinting while driving, Donald went shopping for a pair of sunglasses. He tried glasses with different frames and lenses. Cat eye frames Browline frames Aviator frames Polarized lenses 2 5 2 2 4. 4 Regular lenses What is the probability that a randomly selected pair of sunglasses has regular lenses or cat eye fra Simplify any fractions,

Answer 1

From our table, we have

$P(\text{regular lenses)=}\frac{2+4+4}{19}=\frac{10}{19}$

similarly

$P(\text{cat eye frame)=}\frac{2+2}{19}=\frac{4}{19}$

and the searched probability is

$P(\text{regular lenses }\cup\text{ cat eye frame)=}P(\text{regular lenses)}+P(\text{ cat eye frame)-}P(\text{regular lenses }\cap\text{ cat eye frame)}$

which gives

$\begin{gathered} P(\text{regular lenses }\cup\text{ cat eye frame)=}\frac{10}{19}+\frac{4}{19}-\frac{2}{19} \\ P(\text{regular lenses }\cup\text{ cat eye frame)=}\frac{12}{19} \end{gathered}$

then, the answer is

$P(\text{regular lenses }\cup\text{ cat eye frame)=}\frac{12}{19}$