In a set of 10 aluminum castings,two castings are defective (D),and the remaining eight are good (G).A quality control inspector randomly selects three of the ten castings with replacement,and classifies each as defective (D)or good (G).The sample space for this experiment contains ___ elementary events.
A)1,000
B)720
C)100
D)10
E)3

Question

Quizplus · Accepted Answer

The sample space for this experiment contains 1000 elementary events. This is because each of the three castings can be either defective or good, so there are 2^3 = 8 possible outcomes for each casting. Since the castings are selected with replacement, the order in which they are selected does not matter, so there are 8^3 = 1000 possible outcomes overall.

In a Set of 10 Aluminum Castings,two Castings Are Defective