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 0.1 ​, and the probability that a carton has a puncture and has a smashed corner is 0.006 . 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. ​No, a carton can 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 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 nothing . ​(Type an integer or a decimal. Do not​ round.)

Answer 1

P(carton with a puncture) = 0.06

P(carton has smashed corner) = 0.1

P(carton has a puncture and has a smashed corner) = 0.006

a) Since P(carton has a puncture and has a smashed corner) is not zero, they are not mutually exclusive events.

Option-B) No, a carton can have a puncture and a smashed corner

b) P(carton has a puncture or a smashed corner) = P(carton has a puncture) + P(carton has a smashed corner) - P(carton has a puncture and a smashed corner)

                                                         = 0.06 + 0.1 - 0.006

                                                         = 0.154 (ans)