Respuesta :
Given:
[tex]P(A)=\dfrac{1}{4},P(A\cap B)=\dfrac{1}{12},P(A\cup B)=\dfrac{13}{24}[/tex].
To find:
The value of [tex]P(B)[/tex].
Solution:
We know that,
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
Putting the given values, we get
[tex]\dfrac{13}{24}=\dfrac{1}{4}+P(B)-\dfrac{1}{12}[/tex]
[tex]\dfrac{13}{24}-\dfrac{1}{4}+\dfrac{1}{12}=P(B)[/tex]
[tex]\dfrac{13-6+2}{24}=P(B)[/tex]
[tex]\dfrac{9}{24}=P(B)[/tex]
[tex]\dfrac{3}{8}=P(B)[/tex]
Therefore, the value of [tex]P(B)[/tex] is [tex]\dfrac{3}{8}[/tex].
