Problem 74E

Risk of a natural gas pipeline accident. Process Safety Progress (Dec. 2004) published a risk analysis for a natural gas pipeline between Bolivia and Brazil. The most likely scenario for an accident would be natural gas leakage from a hole in the pipeline. The probability that the leak ignites immediately (causing a jet fire) is .01. If the leak does not immediately ignite, it may result in a delayed ignition of a gas cloud. Given no immediate ignition, the probability of delayed ignition (causing a flash fire) is .01. If there is no delayed ignition, the gas cloud will harmlessly disperse. Suppose a leak occurs in the natural gas pipeline. Find the probability that either a jet fire or a flash fire will occur. Illustrate with a tree diagram.

Answer

Step 1 of 1

The probability that the leak ignites immediately is 0.01.

Given no immediate ignition, the probability of delayed ignition is 0.01.

We need to find the probability that either a jet fire ( leak ignites immediately ) or a flash fire (delayed ignition ) will occur.

We need to Illustrate with a tree diagram.

Lets define the following events:

Let be the event that leak ignites immediately ( Jet fire).

Let B be the event that leak has delayed ignition (flash fire)

We have given the following data,

Hence the probability of either a jet fire or a flash fire,

[addition rule of probability]

Since are mutually exclusive events, hence

We can write

[]

Hence the probability that either a jet fire ( leak ignites immediately ) or a flash fire (delayed ignition ) will occur is

The tree diagram of this problem is: