Let's label the different defects.
B&=paint blemish
D&=dent
We want to find the union of refrigerators having paint blemishes or a dent P(B or D). To calculate this probability, we have to add the probability of each event and subtract their intersection.
P(B or D)=P(B)+P(D)-P(B and D)
From the exercise, we know that 4 % of all refrigerators has paint blemishes, 0.5 % of the refrigerators have dents, and the probability that a refrigerator has both paint blemishes and a dent is also 0.5 %
P(B)&=4 % [0.7em]
P(D)&=0.5 % [0.7em]
P(B and D)&=0.5 %
With this, we can find the probability of the union of the refrigerators having paint blemishes and a dent.
Since the intersection of paint blemishes and dents is the same probability as that of paint blemishes only, we can conclude that any refrigerator with a dent must also have a paint blemish.
