# Discrete Mathematics Test Question

Need help with this question or any other Math homework assignment task or project?

## Popular Services

Post your project now for free and watch professional homework help experts outbid each other in just a few minutes.

## Discrete Mathematics Test Question

Modified
Viewed 18
Part 1: Suppose that F and X are events from a common sample space with P(F) not = 0 and P(X) not = 0. (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 ? F) is another way of writing the definition of conditional probability, and then use that with the logic from the proof of Theorem 4.1.1. (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 users 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. (a) 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?

This order does not have tags, yet.

1
0
{Please find attached the answer. I was happy to help. Best Regards.}