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

$\begin{array}{1 1}(A)\;0.52\\(B)\;0.58\\(C)\;0.32\\(D)\;\text{None of these}\end{array}$

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 B)=P(B')=1-P(B)
$\Rightarrow 1-0.48$
$\Rightarrow 0.52$
Hence (A) is the correct answer.