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.

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.