Question

A screw factory has two machines, the M1, which is old, and does $75\%$ of all the screws, and the M2, newer but small, that does $25\%$ of the screws. The M1 does $4\%$ of defective screws, while the M2 just does $2\%$ of defective screws. If we choose a screw at random: what is the probability that it turns out to be defective?

• A. $0.035$
• B. $0.045$
• C. $0.015$
• D. None of these

Answer 1

The correct option is A $0.035$

The diagrammatic representation of the problem is shown above.

We consider the following events;

$M1=$ being produced by machine $1$.

Therefore, $\overline{M1}=M2$ being produced by machine $2$.

$D=$ defective screw.

In the diagram we can see the red branch in which we are interested.

The top branch being produced by machine $1$ and being defective has probability $\frac{75}{100}\times \frac{4}{100}=0.75\times 0.04=0.03$.

The bottom branch being produced by machine $2$ and being defective has probability $\frac{25}{100}\times \frac{2}{100}=0.25\times 0.02=0.005$.

Therefore, the probability of being defective is $0.03+0.005=0.035$.