Question #411d8

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Answer 1 · 2017-08-25T07:42:21

They are not independent. See explanation.

Two events #A# and #B# are independent if and only if #P(AnnB)=P(A)*P(B)#

In the given question we have:

#P(C) >0#, #P(D)>0#

From this we know that: #P(C)*P(D)>0#.
The information #C# and #D# are disjoint means that they have empty product #P(CnnD)=0#

Combining the above facts we have:

#P(CnnD)=0# and #P(C)*P(D)>0#, so:
#P(CnnD) != P(C)*P(D)#

The above inequality means that the events are not independent.