Laser surgery to fix shortsightedness is becoming more popular. However, for some people, a second procedure is necessary. The following table lists the joint probabilities of needing a second procedure and whether the patient has a corrective lens with a factor (diopter) of minus 8 or less.

Vision Corrective Vision Corrective Factor of Factor of More Than Minus 8 Minus 8 or Less First procedure is successful .66 .15 Second procedure is required .05 .14

a. Find the probability that a second procedure is required.

b. Determine the probability that someone whose corrective lens factor is minus 8 or less does not require a second procedure.

c. Are the events independent? Explain your answer.