Examples

Reliability: Series, parallel, series

Suppose a process has internal components arranged like this:

Write for the event that component succeeds, and for the event that it fails.

The success probabilities for each component are given in the chart:

1	2	3	4	5
92%	89%	95%	86%	91%

Find the probability that the entire system succeeds.

Solution

For intersections, use (independence) and for unions, use .

So and: