For safety and health reasons, Perpetual Mercy Hospital is considering requiring all health care providers to wear latex gloves when interacting with patients. However, the board of directors is going to take a vote, and most of them have a latex allergy. The board of directors consists of 12 nonallergic and 18 allergic members, and 35 percent of the nonallergic members and 70 percent of the allergic members favor the glove policy.
a. Construct a probability tree for this problem.
b. Construct a probability table for this problem.
c. Determine the probability that a board of directors member who opposes the new policy is nonallergic.
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