Chapter 13.CR, Problem 1CR

To determine

To find:

The probability that anyone item is defective from a 1, 000 sampled items which has four defectives.

Answer to Problem 1CR

Solution:

The probability that any one item is defective from a 1, 000 sampled items which has four defectives is $0.004$.

Explanation of Solution

Definition:

If an experiment has n mutually exclusive and equally likely outcomes, and if s is the favorable outcomes, then the probability of any event E denoted as $P\left(E\right)$ is defined as,

$P\left(E\right)=\frac{s}{n}=\frac{\text{Number of outcomes favorable to }E}{\text{Number of all possible outcomes}}$

Calculation:

Consider a sample of 1, 000 items from an assembly line. This sample reveals four defective items from these sampled items.

Define E to be the event that the item is defective. So there are 4 favorable outcomes. Use the probability formula and calculate the probability.

$\begin{array}{rll}P\left(E\right)& =& \frac{\text{Number of outcomes favorable to }E}{\text{Number of all possible outcomes}}\\ & =& \frac{4}{1000}\\ & =& 0.004\end{array}$

Thus, the required probability is $0.004$.

Final statement:

The probability of getting defective item from 1, 000 sampled items is $0.004$.