Question

If \(A\) and \(B\) are two events such that \(P(A)=\frac{1}{4},P(B)=\frac{1}{2}\) and \(P(A∩B)=\frac{1}{8}\),find \(P\) (not \(A\) and not \(B\)).

Answer 1

The correct answer is: \(\frac{3}{8}\)
It is given that; \(P(A)=\frac{1}{4}, P(B)=\frac{1}{2},\)
P(not on A and not on B)=\(P(A'\cap B')\)
P(not A and not on B)=\(P((A\cup B))'\)       \([A'\cap B'=(A\cup B)']\)
\(=1-P(A\cup B)\)
\(=1-[P(A)+P(B)-P(A\cap B)]\)
\(=1-\bigg[\frac{1}{4}+\frac{1}{2}-\frac{1}{8}\bigg]\)
\(=1-\frac{5}{8}\)
\(=\frac{3}{8}\)