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 0.05, the probability that a carton has a smashed comer is 0.06, and the probability that a carton has a puncture and has a smashed corner is 0.003. 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 can have a puncture and a smashed corner. B. No, a carton cannot have a puncture and a smashed corner. C. Yes, a carton cannot have a puncture and a smashed corner. D. Yes, a carton can have a puncture and a smashed comer. (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

Explanation / Answer

Solution:

(a) A. No, a cartoon can have a puncture and a smashed corner.
Events are mutually exclusive when they cannot occur simultaneously.

(b) P(puncture) = 0.05

P(smashed corner) = 0.1

P(puncture and smashed corner) = 0.005
P(puncture or smashed corner) = P(puncture)+ P(smashed corner) - P(puncture and smashed corner) = 0.05+0.1-0.005
= 0.145

The probability that a carton has a puncture or a smashed corner is = 0.145

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