(1) Prove or disprove the following statement: For an event A, if P(A)メ1 and P(A)メ0, then...

Question

Question

(1) Prove or disprove the following statement: For an event A, if P(A)メ1 and P(A)メ0, then A and Ac are independent.

math Statistics-And-Probability

Answer 1

Answer #1

here let P(A) =x and 0<x<1

therefore P(Ac)=1-P(A) =1-x

for A and Ac complement event and therefore they do not contian any common eleement ;

hence P(A n Ac)=0

also P(A)*P(Ac) =x*(1-x) which is not equal to 0 ; as x is not equal to 0 or 1.

hence P(A)*P(Ac) is not equal to P(A n Ac) and therefore not independnet,

Answer 2

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