You are responsible for analyzing flight delays in an airport. From the 100 flights you are monitoring, 35 of them are delayed due to different reasons. You decide to randomly and sequentially select 3 of them to analyze ("sequentially" means you cannot select the same flight multiple times). For all questions below, please show your work and keep 4 significant digits for your answers. a. [1 point] What is the probability that the first flight you chose got delayed? b. [1 point] What is the probability that the third flight is delayed, given that the first two flights chosen are not delayed? c. [2 points] What is the probability that overall, you choose 2 delayed flights and 1 NOT delayed flight?You decide to further analyze the reasons for the delay. There are 3 possible reasons for delay: weather (W), facilities (F), and emergencies (E). Each variable is binary (for example, either W=w or W=w). Based on the analysis, you have the following probability table: Probability (W,F,E) W F P(W,Fle) P(W,F|-e) T T 0.75 0.15 T F 0.15 0.35 F T 0.09 0.0 F F 0.01 0.5 And you know P(e) = 0.4. d. [2 points] Calculate P(W|f). That is, given F=f, provide the probability for P(w|f) and P(-w/f). e. [2 points] Calculate P(w). For safety reasons, the airport must cancel the flight if they find severe problems (S). The probability of a severe problem is P(s) = 1e-7. However, not all problems are reported (R), and not all reports are related to severe problems. The probability that a severe problem gets reported is P(r|s) = 0.999. Meanwhile, the probability of a false positive report is P(r|-s) = 0.1.f. [3 points] Suppose the airport gets a report of a severe problem. What is the probability that the airport really has a severe problem? That is, calculate P(s|r). g. [3 points] Suppose the airport does not get a report of severe problems. What is the probability that the airport has a severe problem that is not reported? That is, calculate P(sl-Ir)