Answer: [tex]P(A) = 0.23[/tex]
Step-by-step explanation:
Given :
[tex]P(A/B) = 0.2[/tex]
[tex]P(A/B^{1})=0.3[/tex]
[tex]P(B)= 0.7[/tex]
[tex]P(A) = ?[/tex]
From rules of probability :
[tex]P(A) = P(AnB) + P(A n B^{1})[/tex] ........................... equation *
[tex]P(A n B)[/tex] can be written as [tex]P(A/B)[/tex] x [tex]P(B)[/tex]
Also , [tex]P(A/B^{1})[/tex] can be written as [tex]P(A/B^{1})[/tex] x [tex]P(B^{1})[/tex]
substituting into equation * , we have
[tex]P(A) = P(A/B)[/tex][tex]P(B) + P(A/B^{1})P(B^{1})[/tex]
since P(B) = 0.7, then [tex]P(B^{1}) = 1 - P(B) = 0.3[/tex]
so , substituting each values , we have
[tex]P(A) = (0.2)(0.7) + (0.3)(0.3)[/tex]
[tex]P(A) = 0.14 + 0.09[/tex]
[tex]P(A) = 0.23[/tex]
