Using the distribution in Exercise 2, let the random variable Y be the number of defects on a contact lens randomly selected from lenses produced during the shift. (a) Find the mean and variance of Y...

Using the distribution in Exercise 2, let the random variable Y be the number of defects on a contact lens randomly selected from lenses produced during the shift.

(a) Find the mean and variance of Y for the shift.

(b) Assume that the lenses are produced independently. What is the probability that five lenses drawn randomly from the production line during the shift will be defect-free?

Exercise 2

The following is a probability distribution of the number of defects on a given contact lens produced in one shift on a production line:

Let A be the event that one defect occurred, and B be the event that 2, 3, or 4 defects occurred. Find:

(a) P(A) and P(B)

(b) P(A and B)

(c) P(A or B)