Question

according to a center for disease control, the probability that a randomly selected person has hearing problems is 0.159. the probability that a randomly selected person has vision problems is 0.082. can we compute the probability of randomly selecting a person who has hearing problems or vision problems by adding these probabilities? why or why not? choose the correct answer below. a. yes, because this is an application of the addition rule for disjoint events. b. no, because hearing and vision problems are not mutually exclusive. so, some people have both hearing and vision problems. these people would be included twice in the probability. c. no, because hearing problems and vision problems are events that are too similar to one another. d. yes, because hearing and vision are two different senses, and therefore, they are two unique problems.

Explanation:

Mutually - exclusive events cannot occur at the same time. Hearing and vision problems are not mutually exclusive as a person can have both simultaneously. If we simply add the probabilities of two non - mutually exclusive events, the people with both problems will be double - counted.

Answer:

B. No, because hearing and vision problems are not mutually exclusive. So, some people have both hearing and vision problems. These people would be included twice in the probability.