Question

Three machines A, B, and C produce 55%, 25% and 20% respectively. The percentages of defective output are 3.5%, 4.5% and 5.5%. If an item is selected randomly, find the probability that the item is defective.

Answer 1

We are given the following information concerning the three production machines;

$\begin{gathered} Of\text{ the total production;} \\ A=55\text{ \%}=0.55 \\ B=25\text{ \%}=0.25 \\ C=20\text{ \%}=0.20 \end{gathered}$

Also, we are given the percentage of defective output as follows;

$\begin{gathered} A=3.5\text{ \%}=0.035 \\ B=4.5\text{ \%}=0.045 \\ C=5.5\text{ \%}=0.055 \end{gathered}$

Therefore, if an item is selected randomly, the probability that the item is defective would be;

$\begin{gathered} P\lbrack defective\rbrack=(0.55\times0.035)+(0.25\times0.045)+(0.20\times0.055) \\ P\lbrack\text{defective\rbrack}=0.01925+0.01125+0.011 \\ P\lbrack\text{defective\rbrack}=0.0415 \end{gathered}$

ANSWER:

The probability that the item is defective would be 0.0415