BAYES THEOREM

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2. In a garden, 40% of the flowers are roses and the rest are carnations. If 25% of the roses and 10% of the carnations are red, find the probability that a red flower selected at random is a rose.3. While watching a game of Champions League football in a cafe, you observe someone who is clearly supporting Manchester United in the game.What is the probability that they were actually born within 25 miles of Manchester ? Assume that: the probability that a randomly selected person in a typical local barenvironment is born within 25 miles of Manchester is 1/20 , and; the chance that a person born within 25 miles of Manchester actuallysupports United is 7/10 ; the probability that a person not born within 25 miles of Manchestersupports United with probability 1/10 .

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