Answer to Question #293641 in Statistics and Probability for hanhanhannnnnnnnn

Question

In a National Achievement Test, suppose three test

booklets are tested at random. Let D represent the

defective test booklet and let N represent the

non-defective test booklet. Let X be the random

variable representing the number of non-defective

test booklets

Answer 1

There are $2^3=8$ possible outcomes

The sample space $S$ is given as, $S=\{DDD,DDN,DND,DNN,NDD,NND,NNN\}$

The random variable $X$ may take on the values, 0,1,2,3. We can express this as, $x=0,1,2,3$  

We shall present the number of non-defective test booklets in the frequency distribution table below,

$X$ $f$

0 1

1 3

2 3

3 1

The probability distribution is,

$x$ 0 1 2 3

$p(x)$ ${1\over8}$ ${3\over8}$ ${3\over8}$ ${1\over8}$