Yes. Independent events can exist in reality. Dependent events means that one event has had an effect on the other. For instance, if we look at the probability of someone going to the shops, and the...
if P(A)>0 then P(B'|A)=1-P(B|A) so P(A intersect B')=P(A)P(B'|A)=P(A)[1-P(B|A)] =P(A)[1-P(B)] =P(A)P(B') the definition of independent events is if P(A intersect B')=P(A)P(B') that is the proof
The occurrence of one event does not affect the occurrence of the other event.
Take for example tossing a coin. The first toss has no affect on the outcome of the second toss, so these events are...