Answer:
A. [tex]P(A\cap B=\frac{14}{15}[/tex]
Step-by-step explanation:
Use the formula;
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
It was given that;
[tex]p(A)=\frac{2}{3}[/tex]
[tex]p(B)=\frac{4}{5}[/tex]
and
[tex]p(A\cup B)=\frac{8}{15}[/tex]
We substitute all these values into the formula to get;
[tex]\frac{8}{15}=\frac{2}{3}+\frac{4}{5}-P(A\cap B)[/tex]
[tex]\frac{8}{15}-\frac{2}{3}-\frac{4}{5}=-P(A\cap B)[/tex]
The least common denominator is 15
[tex]\frac{8-10-12}{15}=-P(A\cap B)[/tex]
[tex]\frac{-14}{15}=-P(A\cap B)[/tex]
Divide both sides by -1.
[tex]\frac{14}{15}=P(A\cap B)[/tex]
[tex]P(A\cap B=\frac{14}{15}[/tex]
