Suppose that If and X are events from a common sample space with F( F) / 0 and P(X ) 4 0

Suppose that If and X are events from a common sample space with F( F) / 0 and P(X ) 4 0. (s) Prove that P(X) - P(XIF)POP) + P(XSIP(IT). Hint: Explain why P(XIAJP( P) - P(Xn F) is another way of writing the definition of conditional probability, and then use that with the logic from the proof of Themran 4.1.1. (b) Explain why PUFIN) - P(XIF)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 & 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 (3). (b) Using Bayes' Theorem, out of users who log on every day, what is the probability that they are from inside the country?