Two events E and F are independent if any one of the following conditions are met: (i) P(E/F)= P(E) (ii)P(F/E)=P(F) (iii)P(E n F)=P(E).P(F)

Rhett Guerrero

Rhett Guerrero

Answered question

2022-11-19

Two events E and F are independent if any one of the following conditions are met:
(i) P ( E / F ) = P ( E )
(ii) P ( F / E ) = P ( F )
(iii) P ( E n F ) = P ( E ) P ( F )
Is it correct to then assume that if E and F are independent having met condition (i) or (ii), then E and F are also mutually exclusive?

Answer & Explanation

Izabella Henson

Izabella Henson

Beginner2022-11-20Added 20 answers

No. Mutually exclusive or disjoint if they cannot both be true.
P ( E | F ) = P ( E F ) P ( F )
As independent event P ( E F ) = P ( E ) P ( F )
= P ( E ) P ( F ) P ( F )
= P ( E )

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