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Unformatted text preview: B should be true with conditional probability one. That is why the
deﬁnition of P (B |A) has P (A) in the denominator.
One of the very nice things about elementary probability theory is the simplicity of this deﬁnition of conditional probability. Sometimes we might get conﬂicting answers when calculating the
probability of some event, using two diﬀerent intuitive methods. When that happens, inevitably,
at least one of the methods has a ﬂaw in it, and falling back on simple deﬁnitions such as the
deﬁnition of conditional probability clears up the conﬂict, and sharpens our intuition.
The following examples show that the conditional probability of an event can be smaller than,
larger than, or equal to, the unconditional probability of the event. (Here, the phrase “unconditional
probability of the event” is the same as the probability of the event; the word “unconditional” is
used just to increase the contrast with conditional probability.)
Example 2.3.1 Roll two dice and observe the numbers coming up. Deﬁne two events by: A=“the
sum is six,” and...
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- Spring '08
- The Land