In a production plant, 20% people are exposed to very loud noises. Of those who are...

In a production plant, 20% people are exposed to very loud noises. Of those who are exposed to loud noises, 10% show sign of hearing loss at some point of their lives. Of those who are not exposed to loud noises, only 5% will develop hearing loss.

a). What is the probability that a randomly chosen person is not exposed to loud noise?

b). What is the probability that a randomly chosen person will experience hearing loss?

c). Are the events "exposed to loud noises" and "person will experience hearing loss" independent? You must show computations to support your answer.

d). Are the events "exposed to loud noises" and "person will experience hearing loss" mutually exclusive (disjoint)? You must show computations to support your answer.

Expert Solution

P(exposed to very loud noises) = 0.2

P(hearing loss | exposed to loud noises) = 0.1

P(hearing loss | not exposed to loud noises) = 0.05

a) P(not exposed to loud noises) = 1 - P(exposed to loud noises) = 1 - 0.2 = 0.8

b) P(hearing loss) = P(hearing loss | exposed to loud noises) * P(exposed to loud noises) + P(hearing loss | not exposed to loud noises) * P(not exposed to loud noises)

= 0.1 * 0.2 + 0.05 * 0.8

= 0.06

c) No, the events "exposed to loud noises" and "person will experience hearing loss" are not independent. Because P(hearing loss | exposed to loud noises) is not equal to P(hearing loss)

d) No, the events "exposed to loud noises" and "person will experience hearing loss" are not mutually exclusive events. Because P(hearing loss and exposed to loud noises) is not equal to zero.

P(hearing loss and exposed to loud noises) = P(hearing loss | exposed to loud noises) * P(exposed to loud noises) = 0.1 * 0.2 = 0.02

orchestra answered 2 years ago

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