Given:
[tex]P(A\cap B)=\dfrac{3}{4}[/tex]
[tex]P(B)=\dfrac{4}{5}[/tex]
To find:
The [tex]P(A|B)[/tex].
Solution:
Conditional probability:
[tex]P(A|B)=\dfrac{P(A\cap B)}{P(B)}[/tex]
Substituting the given values, we get
[tex]P(A|B)=\dfrac{\dfrac{3}{4}}{\dfrac{4}{5}}[/tex]
[tex]P(A|B)=\dfrac{3}{4}\times \dfrac{5}{4}[/tex]
[tex]P(A|B)=\dfrac{16}{16}[/tex]
Therefore, the correct option is B.
