Answer to Question #309105 in Statistics and Probability for Rose

Question

Suppose three test kits are tested at random. Let D represent the defective test kit and let N represent the non-defective test kit. If we let X be the tendon variable for the number of defective test kits, construct the probability distribution of the random variable X

Answer 1

If three test kits are tested there are four possible outcomes:

1. All three are working and none is defective and thus X is 0
2. One is defective and the other two are working and thus X is 1
3. Two are defective and only one is working and thus X is 2
4. All three are defective and thus X is 3

The probability distribution of X is thus:

$\def\arraystretch{1.5}\begin{array}{c:c}X&P(X)\\\hline0&P0\\\hline1&P1\\\hline2&P2\\\hline3&P3\\\hline\end{array}$