5. (10 points) Three airlines (American, Delta, United) serve an airport. The three airlines have 40%, 30%, 30% of all the scheduled flights of the airport respectively. Their on-time rates are 80%, 80%, and 70% respectively. (a) Complete the following probability table for the joint probabilities. American Delta United On time Not on time (b) A plane has just left on time. What is the probability that it was an American Airlines flight? 6. (10 points) Consider the following sample on the newspaper readership and occupation type in a city: Newspaper Occupation G&M Post Star Sun Total Blue collar 27 18 38 37 120 White collar 29 43 21 15 108 Professional 33 51 22 20 126 Total 89 112 81 72 354 (a) Find the unconditional distribution of the newspaper readership, Pr (Newspaper = G&M) , Pr (Newspaper = Post), Pr (Newspaper = Star) , and Pr (Newspaper = Sun) . (b) Find the conditional distribution of the newspaper readership for blue collar workers, Pr (Newspaper = G&M | Occupation = Blue Color) , Pr (Newspaper = Post | Occupation = Blue Color), Pr (Newspaper = Star | Occupation = Blue Color) , and Pr (Newspaper = Sun | Occupation = Blue Color)