7 55% of the patients a psychologist sees are males. Additionally, the psycholog

Question

7 55% of the patients a psychologist sees are males. Additionally, the psychologist has diagnosed 43% of the patients with depression. The psychologist observes that 20% of her patients are males with depression a. What is the probability that a patient is male or depressed? b. Given that a patien is female, what is the probability that she is not depressed c. What is the probability that a patient is female or depressed? d. Are sex and depression status mutually exclusive? Explain e. Are sex and depression status independent? Explain

Explanation / Answer

P(M) = 0.55, P(M') = 0.45
P(D) = 0.43
P(D and M) = 0.2

a)
P(M or D) = P(M) + P(D) - P(D and M)
= 0.55 + 0.43 - 0.2
= 0.78

b)
P(D'|M') = P(D' and M')/P(M')
P(D' and M') = P(D or M)' = 1 - P(D or M) = 1 - 0.78 = 0.22

P(D'|M') = 0.22/0.45 = 0.4889

c)
P(M' or D) = P(M') + P(D) - P(M' and D)
P(M' and D) = P(D) - P(M and D) = 0.43 - 0.2 = 0.23
P(M' or D) = 0.45 + 0.43 - 0.23 = 0.65

d)
No, sex and depression are not mutually exclusive
because P(M and D), P(M' and D) are not equal to zero

e)
No, not independent
because P(M and D) = 0.2 not equals to P(M)*P(D) = 0.55 * 0.43 = 0.2365

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