I need help with 2a (yellow highlight) using the proof of Theorem 4.1.1 from 1a (red circled). ***Please type your answer or write in print, because I have had great difficulty with understanding most handwritten assistance done in cursive or mixed print/cursive. Part 1: Suppose that F and X are events from a common sample space with P(F) +0 and P(X)+0.(a) Prove that P(X)P(X n F) is another way of writing the definition of conditional probability, and then usethat with the logic from the proof of Theorem 4.1.1.P(X|F)P(F) + P(X|F)P(F). Hint: Explain why P(X|F)P(F)(b) Explain why P(F|X) = 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 usersfrom 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.(a) What percent of all users log on every day? Hint: Use the equation from Part 1 (a).

Name: I need help with 2a (yellow highlight) using the proof of Theorem 4.1.
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: I need help with 2a (yellow highlight) using the proof of Theorem 4.1.1 from 1a (red circled). ***Please type your answer or write in print, because I have had great difficulty with understanding most handwritten assistance done in cursive or mixed p

As per bartleby guidelines for more than one question asked only one is to be answered please upload the other separately. To find Part 2: Given that PX=PX|FPF+PX|F¯PF¯ where F and F¯ are mutually exclusive event. Now, Let X be the total percentage of users log on everyday, F be the percentage of users from outside the country log on everyday, and F¯ be the percentage of users from inside the country log on everyday. Let the probability of the total percentage of users log on everyday, P(X)=100x Probability of users log from outside the country, P(F)=70x Probability of users log from inside the country, P(F¯)=30x Probability of users log from outside the country everyday, P(X|F)P(F)=6010070x=42x Probability of users log from inside the country everyday, P(X|F)P(F)=8010030x=24xNow, Total probability of users log on everyday is given by using the proof of Part 1(a), PX=PX|FPF+PX|F¯PF¯P(X)=42x+24x=66xP(X)=66x. Thus, the total percent of users log on everyday is 66%.