SOLUTION: Find the following probabilities: (A)Events A and B are mutually exclusive events defined on a common sample space. If P(A)= 0.4 and P(AorB)=0.75, find P(B). (B) Events A and

Question 334547: Find the following probabilities:
(A)Events A and B are mutually exclusive events defined on a common sample space. If P(A)= 0.4 and P(AorB)=0.75, find P(B).
(B) Events A and B are defined on a common sample space. If P(A)= 0.40, P(B)= 0.50 and P(AorB)= 0.72, find P(AandB).

Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
P(A or B)=P(A)+P(B)-P(A and B)
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a)Events A and B are mutually exclusive events defined on a common sample space. If P(A)= 0.4 and P(AorB)=0.75, find P(B).
Mutually exclusive means both cannot happen thus P(A and B)=0
therefore
P(A or B)=P(A)+P(B)-P(A and B)=P(A)+P(B)
0.75=0.4+P(B)
P(B)=0.75-0.4=0.35
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b) Events A and B are defined on a common sample space. If P(A)= 0.40, P(B)= 0.50 and P(AorB)= 0.72, find P(AandB).
P(A or B)=P(A)+P(B)-P(A and B)
P(A and B)=P(A)+P(B)-P(A or B)=0.40+0.50-0.72=0.18
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