Question: Suppose that E1, E2, . . . , Em are mutually exclusive events such that E1 U E2, U . . .,Em = ¦; that

Suppose that E1, E2, . . . , Em are mutually exclusive events such that E1 U E2, U . . .,Em = „¦; 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.)

Show that PLE, IF}-P{ FE, PIE,}/y p(FE,PEI.

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