In a set of 15 aluminum castings,two castings are defective (D),and the remaining thirteen are good (G).A quality control inspector randomly selects three of the fifteen castings without replacement,and classifies each as defective (D)or good (G).The sample space for this experiment contains ___ elementary events.
A)3,375
B)2,730
C)455
D)15
E)3

Question

Quizplus · Accepted Answer

To find the number of elementary events, we need to calculate the number of ways to choose 3 castings out of 15, and then assign each of those castings as defective or good. This can be done using combinations and multiplication: 
- Number of ways to choose 3 castings out of 15 = 15 choose 3 = (15*14*13)/(3*2*1) = 455 
- For each of these 455 ways, we can assign D or G to each of the 3 castings. This gives us a total of 2^3 = 8 possible outcomes for each of the 455 ways. 
Therefore, the total number of elementary events is 455*8 = 3,640. 
The closest answer choice to 3,640 is C = 455.

In a Set of 15 Aluminum Castings,two Castings Are Defective