CPM Homework Help : CCG Problem 6-75

Refrigerators that are produced on an assembly line sometimes contain defects. The probability a refrigerator has a paint blemish is $4\%$ . The probability that it has a dent is $\frac{1}{2}\%$ . The probability it has both a paint blemish and a dent is also $\frac{1}{2}\%$ . What is the probability a refrigerator has a paint blemish or a dent? What can you conclude about defects on these refrigerators?

Hint:

$\text{P}(A\text{ or }B)=\text{P}(A)+\text{P}(B)-\text{P}(A\text{ and }B)$

Answer:

$P(\text{Blemish or Dent)}=P(\text{Blemish)}+P(\text{Dent)}-P(\text{BlemishandDent)}$

$\text{P(Blemish or Dent)}=4\%+0.5\%-0.5\%$
$\text{P(Blemish or Dent)}=4\%$

Conclusion: If a refrigerator has a dent it also always has a paint blemish.