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    Probability help

    Show that if one event A is contained in another event B, then P(A) _< P(B). Hwat does this imply about the relationship between P(AUB), P(A), and P(A inersect B)?
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    Quote Originally Posted by statman101 View Post
    Show that if one event A is contained in another event B, then P(A) _< P(B). Hwat does this imply about the relationship between P(AUB), P(A), and P(A inersect B)?
    If each of C~\&~D is an event then C \cap D = \emptyset \; \Rightarrow \;P(C \cup D) = P(C) + P(D).
    Consider this:  B = A \cup \left( {B\backslash A} \right)\;\& \;A \cap \left( {B\backslash A} \right) = \emptyset .
    So, P(B) = P(A) + P(B\backslash A) \geqslant P(A)\text{, because }P(B\backslash A) \geqslant 0
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