A company that makes cartons finds that the probability of producing a carton with a puncture is 0.04, the probability that a carton has a smashed comer is 0.1, and the probability that a carton has a puncture and has a smashed corner is 0.004. Answer parts (a) and (b) below
(a) Are the events "selecting a carton with a puncture" and "selecting a carton with a smashed cormer mutually exclusive? Explain.
A. Yes, a carton cannot have a puncture and a smashed corner
B. Yes, a carton can have a puncture and a smashed corner y
C. No, a carton can have a puncture and a smashed corner.
D. No, a carton cannot have a puncture and a smashed corner.
(b) If a quality inspector randomly selects a carton, find the probability that the carton has a puncture or has a smashed comer. The probability that a carton has a puncture or a smashed corner is (Type an integer or a decimal. Do not round.) ?

To be mutually exclusive, the probability of the two events happening at the same time should be 0. But the probability that a carton has a puncture and has a smashed corner is 0.004 and not 0.

Then, we can conclude the events "selecting a carton with a puncture" and "selecting a carton with a smashed corner" are not mutually exclusive.

The answer is "C. No, a carton can have a puncture and a smashed corner."

We can calculate the probability that the carton has a puncture or has a smashed comer simply by adding the probability of each event:

[tex]P(X\cup Y)=P(X)+P(Y)=0.1+0.04=0.104[/tex]

P(X ∪ Y): probability that a carton has a puncture or a smashed corner.