A company that makes cartons finds that the probability of producing a carton with a puncture is 0.04, the probability that a carton has a smashed comer is 0.1, 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 cormer mutually exclusive? Explain.
A. Yes, a carton cannot have a puncture and a smashed corner
B. Yes, a carton can have a puncture and a smashed corner y
C. No, a carton can have a puncture and a smashed corner.
D. No, a carton cannot 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 comer. The probability that a carton has a puncture or a smashed corner is (Type an integer or a decimal. Do not round.) ?

a) C. No, a carton can have a puncture and a smashed corner.

b) The probability that a carton has a puncture or a smashed corner is P(X ∪ Y) = 0.104.

Step-by-step explanation:

To be mutually exclusive, the probability of the two events happening at the same time should be 0. But the probability that a carton has a puncture and has a smashed corner is 0.004 and not 0.

Then, we can conclude the events "selecting a carton with a puncture" and "selecting a carton with a smashed corner" are not mutually exclusive.

The answer is "C. No, a carton can have a puncture and a smashed corner."

We can calculate the probability that the carton has a puncture or has a smashed comer simply by adding the probability of each event:

P(X ∪ Y): probability that a carton has a puncture or a smashed corner.

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3

answer: 72: 111

step-by-step explanation: