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The probability that at least one of the two events A and B occurs is 0.6.If A and B occur simultaneously with probability 0.3,evaluate $P(\bar{A})+P(\bar{B})$.

">P($\ Toolbox: • P(at least one of A and B occeure)=P(A\(\cup$B)                 $Also\;\overline{A\cup\;B}=\bar{A}\cap\;\bar{B}$
• P(simultuneous occurance of AandB)=P(A$\cap$B)           $Also\;\overline{A\cap\;B}=\bar{A}\cup\;\bar{B}$
P(A$\cap$B)=0.6
P($\overline{A\cup\;B}$)=1-0.6=0.4
P($\bar{A}$$\cap$$\bar{B}$)=0.4
P(A$\cap$B)=0,3
P($\overline{A\cap\;B}$)=1-0.3=0.7
P($\bar{A}\cup$$\bar{B}$)=P($\bar{A}$)+P($\bar{B}$)-P($\bar{A}$$\cap$$\bar{B}$)
0.7=P($\bar{A}$)+P($\bar{B}$)-0.4
P($\bar{A}$)+P($\bar{B}$)=1.2

edited Mar 16, 2013