Answer:
[tex]\large\boxed{C)\ \dfrac{3}{4}}[/tex]
Step-by-step explanation:
[tex]\text{We know:}\ P(A')=1-P(A)\\\\\text{Therefore}\\\\P(A)-3\cdot P(A')=0\iff P(A)-3\cdot(1-P(A))=0\\\\\text{use the distributive property}\ a(b+c)=ab+ac\\\\P(A)+(-3)(1)+(-3)(-P(A))=0\\\\P(A)-3+3P(A)=0\qquad\text{add 3 from both sides}\\\\P(A)+3P(A)=3\\\\4P(A)=3\qquad\text{divide both sides by 4}\\\\P(A)=\dfrac{3}{4}[/tex]
