Question

Suppose $3$ bulbs are selected at random from a lot. Each bulb is tested and classified as defective $\left(D\right)$ or non-defective $\left(N\right)$. The sample space of this experiment is:

• A. $\{DNN,NDN,NND,NNN\}$
• B. $\{DDD,NNN\}$
• C. $\{DDN,DND,NDD,DNN,NDN,NND\}$
• D. $\{DDD,DDN,DND,NDD,DNN,NDN,NND,NNN\}$

Answer 1

The correct option is D $\{DDD,DDN,DND,NDD,DNN,NDN,NND,NNN\}$

From the question,
$D$ denotes the event of bulb is defective and $N$ denotes the event of non-defective bulbs .
Then, total number of elements in sample space $=2\times 2\times 2=8$
Thus, sample space is obtained as: $S=\{DDD,DDN,DND,NDD,DNN,NDN,NND,NNN\}$