Similarly since ab 1 5 2 4 4 2 5 1 we have

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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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