Question

A and B are events such that $P\left(A\right)=0.3,P(A\cup B)=0.8$. If A and B are independent then P(B)=

• A. $\frac{1}{7}$
• B. $\frac{3}{7}$
• C. $\frac{5}{7}$
• D. $\frac{6}{7}$

Answer 1

The correct option is C $\frac{5}{7}$

Since A and B are independent events, we have $P(A\cap B)=P\left(A\right).P\left(B\right)WeknowP(A\cup B)=P\left(A\right)+P\left(B\right)-P\left(A\right)P\left(B\right)Substitutingthevalues,weget0.8=0.3+P\left(B\right)(1-0.3)0.5=P\left(B\right)\left(0.7\right)\Rightarrow P\left(B\right)=\frac{5}{7}$