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.

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 youranswer.

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