Given:
Total persons, n(S)=80.
Let P(A) be the probability of selecting a person from females.
Let P(B) be the probability of selecting a person from suwanee.
From the table value,
We have,
[tex]\begin{gathered} n(A)=30 \\ n(B)=24 \\ n(A\cap B)=8 \end{gathered}[/tex]
To determine the probability P(Female or Suwanee):
We know that the formula,
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
Find P(A), P(B) and P(A and B):
[tex]\begin{gathered} P(A)=\frac{n(A)}{n(s)} \\ =\frac{30}{80} \end{gathered}[/tex][tex]\begin{gathered} P(B)=\frac{n(B)}{n(s)} \\ =\frac{24}{80} \end{gathered}[/tex]
[tex]\begin{gathered} P(A\cap B)=\frac{n(A\cap B)}{n(s)} \\ =\frac{8}{80} \end{gathered}[/tex]
Hence, using the formula we get,
[tex]\begin{gathered} P\mleft(Female(or)Suwanee\mright)=\frac{30}{80}+\frac{24}{80}-\frac{8}{80}_{} \\ =\frac{46}{80} \\ =\frac{23}{40} \end{gathered}[/tex]
Hence, the probabaility of selecting a person either female or suwanee is,
[tex]\frac{23}{40}[/tex]
Therefore, the correct option is A.
