Mutually exclusive events

Mutually exclusive events

Events are said 'to be mutually exclusive or incompatible if the happening of anyone of them precludes the happening of all the others (i.e., if no two Or more of them can happen simultaneousIy in the same. trial-For example:
(i) In throwing a die all the 6 faces'numbered 1 to 6 are mutually exclusive since if anyone of these faces comes, ,the possibility of others, in the same trial, is ruled out
(ii) Similarly in tossing it coin the events head and tail are mutually exclusive.

 Equally likely events. 

Outcomes of a trial are set to be equally likely if taking into consideration all the 'relevant evidence there is no reason to expect one in preference-to the others. For example w
(i) In tossing an·unbiased or uniform come, head or tail are equally likely events. •
(ii) In throwing an unbiased die, all the six faces are equally likely to'come.

Independent events. 

Several events are said 'to be independent if the happening (or non-happening) of an 'event is 'not affected by the supplementary knowledge concerning the occurrence of any number of the remaining events. For example .
(i) In tossing an unbiased coin the event of. getting a head in the first toss is independent of getting a head,in the second, third and subsequent throws.
(ii) if we draw a card from ,a pack of well-shuffled cards and.replace it before drawing. the second card, the result of the second draw is independent of the first draw. But, however, if the first card drawn is not replaced then the second draw is dependent on the first draw.