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Suppose that 30 percent of the bottles produced in a certain plant are defective. If a bottle is defective, the probability is 0.9 that an inspector will notice it and remove it from the filling line. If a bottle is not defective, the probability is 0.2 that the inspector will think that it is defective and remove it from the filling line.
a. If a bottle is removed from the filling line, what is the probability that it is defective?
b. If a customer buys a bottle that has not been removed from the filling line, what is the probability that it is defective?

Respuesta :

MrRoyal

The probability that a bottle on the line is defective and removed is 0.27 and the probability that a bottle on the line is defective and not removed is 0.03

The probability that a bottle on the line is defective?

The given parameters are:

  • P(Defective) = 30%
  • P(Remove) = 0.9
  • P(Not defective and remove) = 0.2

The probability that a bottle on the line is removed if defective is:

P = P(Defective) * P(Remove)

This gives

P = 30% * 0.9

Evaluate

P = 0.27

Hence, the probability that a bottle on the line is defective and removed is 0.27

The probability that a bottle not on the line is defective?

This probability is represented as:

Defective and Not removed

It is calculated as:

P = P(Defective) * P(Not Remove)

Using the complement rule, the probability that a defective bottle would not be removed is:

P(Not Remove) = 1- P(Remove)

P(Not Remove) = 1 - 0.9 = 0.1

So, we have:

P = 30% * 0.1

Evaluate

P = 0.03

Hence, the probability that a bottle on the line is defective and not removed is 0.03

Read more about probability at:

https://brainly.com/question/251701

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