Question

The scientists of the space station realize that oxygen level is dropping.

• There are 3 possible issues (mutually-exclusive) that can cause oxygen levels to go down: a leak in the fuselage (L), problems with oxygen pump (U), potential malfunctioning of a CO2 filter (F).

• In other words, some malfunction happens and as a result you might have an oxygen leak.

• Based on previous experiences, in case there is any malfunctioning:

P(L) = 0.02, P(U) = 0.49 and P(F) = 0.49.

• The simulation results provide a following data for the conditional probabilities on oxygen leaks (event O – oxygen leak):

P(O|L) = 1

P(O|U) = 0.4

P(O|F) = 0.6

a. Draw a tree diagram that can explains all possible causes of oxygen leakage. Mark the edges of the tree diagram using the values provided in the problem description.

b. Find the probability of oxygen leakage when malfunction is present, i.e. find P(O).

c. Find posterior distributions for each of the causes: P(L|O), P(U|O) and P(F|O).

d. What is the probability that the oxygen leaks are caused either by the problems with pump, or by the problems with filter.

Answer 1