6 help with stats hw The most likely scenario for an acciden

The most likely scenario for an accident for a natural gas pipeline is natural-gas leakage from a hole in the pipeline. The probability that the leak ignites immediately (I) causing a jet fire is 0.22. If the leak does not immediately ignite, it may result in the delayed ignition (D) of a gas cloud. If there is no delayed ignition, the gas cloud will disperse harmlessly (H). Given no immediate ignition, the probability of delayed ignition causing a flash fire is 0.22. Suppose a leak occurs in the natural-gas pipeline. The probability that either a jet fire or a flash fire will occur is (Round to four decimal places as needed.) Illustrate with a tree diagram. Choose the correct answer below.

Solution

a) is wrong because if the leaks ignites inmediately there is no way that result delayed ignition

b) is wrong to the end because the outcome will be I(prime) intercep with D for the first branch

c) is correct

probability that a jet fire will occur is 0.22

probability that a flash fire will ocurr is 0.78*0.22 =0.1716

so the probability that either a jet fire or a flash fire will ocur is 0.1716+0.22 = 0.3916