Discrete mathematics - I finished part two of the question, but I am stuck on explaining and justifying part one, please help.

6 MAT 230 Exam Two - Online La Te X C D overleaf.com/project/5f83ac7667af360001bde610 9 GS 1# lli Apps M Gmail YouTube 9 Maps Translate P Parchment Exchang. 6 Menu MAT 230 Exam Two Ab Review Share Submit History Chat &Recompile Figure 2.png PROBLEM 1 Figure 3.png This question has 2 parts. Figure 4.png Part 1: Suppose that F and X are events from a common sample space with P(F) / 0 and P(X) / 0. Figure 5.png (a) Prove that P(X) = P(X|F)P(F) + P(X|F)P(F). Hint: Explain why P(X|F)P(F) = P(X n F) is another way of writing the definition of conditional probability, and then use Figure 6.png that with the logic from the proof of Theorem 4.1.1. Figure 7.png Figure 8.png Figure 9.png (b) Explain why P(FIX) = P(XIF)P(F)/P(X) is another way of stating Theorem 4.2.1 Bayes' Theorem. hass.png i main.tex New Hasse.PNG Part 2: A website reports that 70% of its users are from outside a certain country. Out of their users prim.png from outside the country, 60% of them log on every day. Out of their users from inside the country, 80% of them log on every day. snhu_logo.png (a) What percent of all users log on every day? Hint: Use the equation from Part 1 (a). Let total = 100x outside country = 70x inside country = 30x Alog on outside = 60/100 (70x) = 42x log on inside = 80/100(30x) = 24x log on everyday = 42x + 24x = 66x Then, as a percentage = 66% (b) Using Bayes' Theorem, out of users who log on every day, what is the probability that they are from inside the country? Bayes Theorem P(B/A) = P(B cap A)/P(A) v File outline i P(B cap A) [both logon and inside] = 24x P(A) (total) = 66x Problem 1 2P(B/A) = 24/66 = 4/11 Part 1: Part 2: v Problem 2 Part 1: Part 2: Problem 3 Problem 4 Problem 5 Problem 6