Find the following probabilities: (A) Events A and B are mutually exclusive even

Question

Find the following probabilities:

(A) Events A and B are mutually exclusive events defined on a common sample space. If P (A) = 0.5 and P(A or B) = 0.75, find P(B).

(B) Events A and B are defined on a common sample space. If P(A) = 0.30, P(B) = 0.50, and P(A or B) = 0.70, find P(A and B)

Explanation / Answer

(A)given that A and B are mutually exclusive events i.e p(A and B)=f                                 P(A)=0.5,P( A or B )=0.75. we know the formula p(A or B)=p(A)+P(B)-P(A and B)             I.e 0.75=0.5+p(B) =>P(B)=0.75-0.5=0.25.                                                                         ?P(B)=0.25.                                                                                                                 (B)Here we use above formula p(A or B)=P(A)+P(B)-P(A and B),substitute the given values in this eqation ,we get 0.70=0.30+0.50-P(A and B)=>P(A and B)=0.1,                                 ?P(A and B)=0.1

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