Question 4: 30% of people caught the flu this year. 80% of people got the flu shot. 20% of the people who got the flu shot still caught the flu. 1 a) Use the definition of conditional probability and any result we've seen in class to prove: Pr(A)=Pr(AB)Pr(B)+Pr(AB)Pr(B) b) What is your probability of catching the flu if you did not get the flu shot? c) Use the definition of conditional probability to prove Bayes' Theorem: Pr(AB)=Pr(B)Pr(BA)Pr(A) d) You know someone who caught the flu. What is the probability that they got the flu shot