if E and F are two independent events ,prove that E` and F` are independent - Maths - Probability

Question

if E and F are two independent events ,prove that E` and F` are
independent

Shivam Mishra · Accepted Answer

Solution :

Basic knowledge: PX+PX'=1 or PX=1-PX'As E and F are independent events, hencePE∩F=PE×PF ;iNowWe know that:PE'∩F'=PEUF'   DeMorgan's Law=1-PE∪F=1-PE+PF-PE∩F=1-PE+PF-PE×PF  Using i=1-PE-PF-PE×PF=1-PE -PF1-PE=1-PE1-PF=PE'×PF'AsPE'∩F'==PE'×PF'Hence E' and F' will also be independent events
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