Suppose that E1 E2 Em are
Suppose that E1, E2, . . . , Em are mutually exclusive events such that E1 U E2, U . . .,Em = Ω; that is, exactly one of the E events will occur. Denote by F any event in the sample space. Note that
and that FE1, i = 1, 2, . . . , m, are also mutually exclusive.
(a) Show that
(b) Show that
(This result is called Bayes’ formula and is useful when it is known that the event F has occurred and there is interest in determining which one of the Et also occurred.)
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