Find the following probabilities: a) Events A & B are mutually exclusive eventsd

Question

Find the following probabilities:
a) Events A & B are mutually exclusive eventsdefined on a common sample space. If P(A)= 0.4and     P(A or B)= 0.75, find P(B). b) Events A and B are defined on a common sample space. IfP(A) = 0.40, P(B) =0.50,and               P(A or B) = 0.72, find P(A and B). Find the following probabilities:
a) Events A & B are mutually exclusive eventsdefined on a common sample space. If P(A)= 0.4and     P(A or B)= 0.75, find P(B). b) Events A and B are defined on a common sample space. IfP(A) = 0.40, P(B) =0.50,and               P(A or B) = 0.72, find P(A and B).

Explanation / Answer

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we know that P(A or B) = P(A) + P(B) - P(A and B) 0.75 = 0.4 + P(B) - 0.0 P(B) = 0.75 - 0.4 =0.35
b) we know that P(A or B) = P(A) + P(B) - P(A andB) 0.72= 0.40 + 0.50 - P(A and B) 0.40 + 0.50 - P(A and B) = 0.72 0.90- P(A and B) = 0.72 - P(A and B)= 0.72-0.90 P(A and B)= -(-0.18) =0.18

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