A flywheel is attached to a crankshaft by 12 bolts, numbered 1 through 12. Each bolt is checked to determine whether it is torqued correctly. Let A be the event that all the bolts are torqued correctly, let B be the event that the #3 bolt is not torqued correctly, let C be the event that exactly one bolt is not torqued correctly, and let D be the event that bolts #5 and #8 are torqued correctly. State whether each of the following pairs of events is mutually exclusive.
a. A and B
b. B and D
c. C and D
d. B and C
(a) A and B are mutually exclusive, since it is impossible for both events to occur.
(b) If bolts #5 and #8 are torqued correctly, but bolt #3 is not torqued correctly, then events B and D both occur.
Therefore B and D are not mutually exclusive.
(c) If bolts #5 and #8 are torqued correctly, but exactly one of the other bolts is not torqued correctly, then events C and D both occur. Therefore C and D are not mutually exclusive.
(d) If the #3 bolt is the only one not torqued correctly, then events B and C both occur. Therefore B and C are not mutually exclusive.
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