elemprob-page6 - Suppose there are 200 men, of which 100...

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Unformatted text preview: Suppose there are 200 men, of which 100 are smokers, and 100 women, of which 20 are smokers. What is the probability that a person chosen at random will be a smoker? The answer is 120 / 300. Now, let us ask, what is the probability that a person chosen at random is a smoker given that the person is a women? One would expect the answer to be 20 / 100 and it is. What we have computed is number of women smokers number of women = number of women smokers / 300 number of women / 300 , which is the same as the probability that a person chosen at random is a woman and a smoker divided by the probability that a person chosen at random is a woman. With this in mind, we make the following definition. If P ( F ) > 0, we define P ( E | F ) = P ( E F ) P ( F ) . P ( E | F ) is read the probability of E given F . Note P ( E F ) = P ( E | F ) P ( F ). Suppose you roll two dice. What is the probability the sum is 8? There are five ways this can happen: (2 , 6) , (3 , 5) , (4 , 4) , (5 , 3)...
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