Phobophobia is a rare affliction in which the victim is afraid of developing a p

Question

Phobophobia is a rare affliction in which the victim is afraid of developing a phobia (you can't make this stuffup!). Suppose that: A person selected at random lias phobophobia with probability 1/100. A person with phobophobia has shaky hands with probability 9/10. A person without phobophobia has shaky hands with probability 1/20. What is the probability that a person selected at random has phobophobia, given that he or she does not have shaky hands? Are the two events "a person has phobophobia" and "a person does not have shaky hands" independent events, or not? Provide justification.

Explanation / Answer

A - a person has phobia = prob = 1/100

P(AB) - A person has shaky hands and Phobia = 9/10

P(A'B) = 1/20

P(ABuA'B) = 9/10+1/20 = 19/20

b)

Or P(B) = 19/20

P(B') = Person not having shaky hands = 1/20

P(AB') = 1/10+99/100(1/20) = 299/2000

P(A)P(B') = 1/20x1/100 not equal to P(A) P(B')

Hence A and B' are not independent.

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