Answer to Question #207242 in Statistics and Probability for Kll

Question #207242

even A and B are such that P(A U B )=0.76,P(B)=0.4 Given that A and B are non mutually exclusive events that are independent calculate P(A)


1
Expert's answer
2021-06-16T06:21:28-0400

AA and BB are non mutually events: P(AB)0.P(A\cap B)\not=0.

AA and BB are independent events: P(AB)=P(A)P(B).P(A\cap B)=P(A)P(B).



P(AB)=P(A)+P(B)P(AB)P(A\cup B)=P(A)+P(B)-P(A\cap B)

=P(A)+P(B)P(A)P(B)=P(A)+P(B)-P(A)P(B)

P(A)=P(AB)P(B)1P(B)P(A)=\dfrac{P(A\cup B)-P(B)}{1-P(B)}

=0.760.410.4=0.6=\dfrac{0.76-0.4}{1-0.4}=0.6

P(A)=0.6P(A)=0.6



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