# A and B are events such that $P(A)=0.42,P(B)=0.48,$P(A and B)=0.16.Determine P(not A)

$\begin{array}{1 1}(A)\;0.48\\(B)\;0.58\\(C)\;0.38\\(D)\;\text{None of these}\end{array}$

Toolbox:
• The formula used to solve this problem $P(A \cup B)=P(A)+P(B)-P(A \cap B)$
Step 1:
P(A)=0.42
P(B)=0.48
P(A and B)=0.16
Step 2:
P(not A)=1-P(A)
We know that P(A)+P(A')=1
$\therefore 1-P(A)=1-0.42$
$\Rightarrow 0.58$
Hence (B) is the correct answer.