A company that makes cartons finds that the probability of producing a carton wi

Question

A company that makes cartons finds that the probability of producing a carton with a puncture is 0.06, the probability that a carton has a smashed corner is 0.08, and the probability that a carton has a puncture and has a smashed corner is 0.005. Answer parts (a) and (b) below.

(a) Are the events "selecting a carton with a puncture" and "selecting a carton with a smashed corner" mutually exclusive? Explain.
A.No, a carton cannot have a puncture and a smashed corner.
B.Yes, a carton cannot have a puncture and a smashed corner.
C.Yes, a carton can have a puncture and a smashed corner.
D.No, a carton can 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 corner.
The probability that a carton has a puncture or a smashed corner is ?
(Type an integer or a decimal. Do not round.)

Explanation / Answer

(a) Since both events can take place simultaneously, the events are not mutually exclusive.

The correct answer is D.No, a carton can have a puncture and a smashed corner.

b. Let A denote the event that the carton has a puncture and B the event that it has a smashed corner

P(A U B) = P(A) + P(B) - P(A B)

= 0.06 + 0.08 - 0.005

= 0.135

The probability that a carton has a puncture or a smashed corner is 0.135

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