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 0.03. the probability that a carton has a smashed comer is 0.09. and the probability that a carton has a puncture and has a smashed corner is 0.003. Answer parts (a) and (b) below. Are the events "selecting a carton with a puncture" and "selecting a carton with a smashed comer" mutually exclusive? Explain. No, a carton cannot have a puncture and a smashed corner. Yes, a carton cannot have a puncture and a smashed corner. No, a carton can have a puncture and a smashed corner. Yes, a carton can have a puncture and a smashed corner. 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

Explanation / Answer

Let

P = has puncture
C = smashed corner

a)

As

P(P n C) = 0.003 =/= 0, then they are not mutually exclusive. Hence,

OPTION C: No, a carton can can have a puncture and a smashed corner. [ANSWER]

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b)

P(P U C) = P(P) + P(C) - P(P n C) = 0.03 + 0.09 - 0.003 = 0.117 [ANSWER]

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