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

Answer

Step 1 of 5</p>

A flywheel is attached to a crankshaft by 12 bolts

Let A be the event that all the bolts are torqued correctly

Let B be the event that #3 bolt is not torqued correctly

Let C be the event that exactly one bolt is not torqued correctly

Let D be the event that #5 and #8 bolts are torqued correctly

Step 2 of 5</p>

Mutually exclusive means both cannot occur

a) Here event A and B are mutually exclusive

Because it is not possible both will not that A and B will occur same time

Step 3 of 5</p>

b) Here event B and D are not mutually exclusive

Because it is possible that the two events B and D to happen at the same time

that #3 is not torqued correctly and #5 and #8 are torqued correctly