Question

If $P\left(A\right)=0.7$ and $P(A\cap B)$ = 0.5 find
1. $P(A-\overline{B}$)
2. $P(\overline{A}\cup B)$

Answer 1

1. $P(A-\overline{B})=P\left(A\right)-P(A\cap \overline{B})P(A-\overline{B})=0.7-P(A-\overline{B})2P(A-\overline{B})=0.7P(A-\overline{B})=\frac{0.7}{2}=0.35$

2. $P(\overline{A}\cup B)=1-P\left(\overline{\overline{A}\cup B}\right)=1-P(A\cap \overline{B})=1-P(A-\overline{B})=1-0.35=0.65$