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Suppose that , and X are events from a common sample space with P(F) / 0 and P(X ) / 0

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Suppose that , and X are events from a common sample space with P(F) / 0 and P(X ) / 0. (s) Prove that P(X ) - P(X(F)P(F) + P(X|P)P(F). Hint: Explain why P(X[MP(F) P(X n F) is another way of writing the definition of conditional probability, and then use that with the logic from the proof of Theoren 4.1.1. (b) Explain why P(FIX) - P(X|F)P(F)/P(X) is another way of stating Theorem 4.2.1 Bayes' Theorem. Part 2: A website reports that 70%% of its users are from outside a certain country. Out of their users from outside the country, 50%% of them log on every day Out of their users from inside the country, 80%% of them log on every day. (2) What percent of all users log on every day? Hint: Use the equation from Part 1 (a). (b) Using Bayes' Theorem, out of users who log on every day, what is the probability that they are from inside the country?