A load test is performed on three wooden trusses in successi

A load test is performed on three wooden trusses in succession. Let C denote the event that a truss survives the load test, so that C c is the event that the truss fails the load test. Thus, for example, one possible outcome is CCcC, which means that the first and last truss survived the load test while the second failed the test.

a) List the elements of the sample space of all possible outcomes of the three load tests.

b) List the elements that constitute each of the following events;

A1 : at least one truss survives the load test,

A2 : all three trusses survive the load test,

A3 : only one truss survives the load test.

c) Are A1 and A2 disjoint? Why?

d) Are A1 and A3 disjoint? Why?

e) Are A2 and A3 disjoint? Why?

Solution

a)

The sample space will consist of following 8 outcomes.

{ CCC ,CCCc , CCcC , CcCC , CCcCc, CcCcC, CcCCc, CcCcCc }.

b)

A1

In this case we will only discard the event where no truss passes the load test.

A1: { CCC, CcCC, CCCc, CCcC, CcCcC, CcCCc, CCcCc }

A2

In this case the only element will be the one in which all of the three trusses survive the load test.

A2:{ CCC }

A3

In this case only those outocmes will be there where one truss survives the load test and two did not.

A3: {CCcCc, CcCcC, CcCCc}

Two events are disjoint if there is no common element in them.

c)

A1 and A2 are not disjoint since CCC is common in both of them.

d)

A1 and A3 are not disjoint beacuse there are 3 elements common in them.(CCcCc, CcCcC, CcCCc)

e)

A2 and A3 are disjoint since there is no common element in them.