ed 5. The probability that a subject has a certain stomach bac- teria is 0.75, the probability that a subject is showing signs of gastritis is 0.15, and the probability that a sub- ed ject both has the bacteria and shows signs of gastritis is 0.09. (a) Find the probability that a subject either shows signs ob- of gastritis, or has the stomach bacteria, or both (the union) ob- (b) If a subject has the stomach bacteria, what is the probability that they show signs of gastritis? ted (c) If a subject does not have the stomach bacteria, what is the probability that they show signs of gastritis? cted (d) If a subject shows signs of gastritis, what is the prob- ability they have the stomach bacteria? ouse (e) Are the events of having the stomach bacteria and showing signs of gastritis independent? se is 6. Answer the following questions with TRUE or FALSE. they It is good practice to explain your answers. the (a) The intersection of two events A and B can be larger than the union of the same two events A and B. itive (b) The probability of a single event A must be smaller than or equal to the union of two events A and B. itive. c) The condition probability of A given B must be Pos- smaller than the intersection of the same two events A and B nega- (d) If two events are independent, that means P{ A or B} = P{A and B } le, in relief:Book Homework 1. Consider the following contingency (frequency) table, in which two species of mice were tested for a specific par- asite: Infected Not Infected Species 1 40 25 Species 2 19 35 (a) Estimate the probability that a randomly selected mouse was species 1. (b) Estimate the probability that a randomly selected mouse was infected. (c) Estimate the probability that a randomly selected mouse was both infected and species 1. (d) Estimate the probability that a randomly selected mouse was not infected and species 2. 2. Continue with the data from Problem 1. (a) If a mouse was species 1, what is the estimated prob- ability they were infected? (b) If a mouse was species 2, what is the estimated prob- ability they were infected? (c) What is the estimated probability that an infected mouse was species 1? (d) What is the estimated probability that an infected mouse was species 2? (e) Are the events that a mouse is species I and a mouse was infected independent