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Q4 (7 p.) Let Asubseteq B and P(A)=P(B)=0.2 Then which of the following is alway TRUE (A) Acap B=emptyset (B) P(Acup B)=P(A) (C) A and B are independent D P(A-B)=0 (E) none of the above.
Çözüm
4.4
(240 Oylar)
Vedat
Elit · 8 yıl öğretmeni
Uzman doğrulaması
Cevap
The correct answer is (B)
.Explanation:Given that
and
, we can analyze each option:(A)
: This is not always true. Since
, there may be some elements in
that are also in
, so
is not necessarily empty.(B)
: This is always true. Since
, the union of
and
is simply
. Therefore,
.(C) A and B are independent: This is not always true. Independence of events depends on the relationship between the events, and in this case,
, so they are not independent.(D)
: This is not always true.
represents the set of elements in
but not in
. Since
, there may be elements in
that are not in
, so
is not necessarily zero.(E) none of the above: This is not the correct answer, as option (B) is always true.Therefore, the correct answer is (B)
.