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.

The correct answer is (B) $P(A\cup B)=P(A)$.<br /><br />Explanation:<br />Given that $A\subseteq B$ and $P(A)=P(B)=0.2$, we can analyze each option:<br /><br />(A) $A\cap B=\emptyset$: This is not always true. Since $A\subseteq B$, there may be some elements in $A$ that are also in $B$, so $A\cap B$ is not necessarily empty.<br /><br />(B) $P(A\cup B)=P(A)$: This is always true. Since $A\subseteq B$, the union of $A$ and $B$ is simply $B$. Therefore, $P(A\cup B)=P(B)=0.2$.<br /><br />(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, $A\subseteq B$, so they are not independent.<br /><br />(D) $P(A-B)=0$: This is not always true. $A-B$ represents the set of elements in $A$ but not in $B$. Since $A\subseteq B$, there may be elements in $A$ that are not in $B$, so $P(A-B)$ is not necessarily zero.<br /><br />(E) none of the above: This is not the correct answer, as option (B) is always true.<br /><br />Therefore, the correct answer is (B) $P(A\cup B)=P(A)$.