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 corner is 0.08, 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 corner" mutually exclusive? Explain 0 A. No, a carton can have a puncture and a smashed corner. B. Yes, a carton can have a puncture and a smashed corner. C. No, a carton cannot have a puncture and a smashed corner. D. Yes, a carton cannot have a puncture and a smashed corner. sa s 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: producing a carton with a puncture

B: carton has smashed corner

P(A)=0.05

P(B)=0.08

P(A and B)=0.004

a) For mutually exclusive events, the P(A and B)=0, thus A is correct since it is given that P(A and B)=0.004

b) P(A or B)=P(A)+P(B)-P(A and B)=0.05+0.08-0.004=0.126

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