In: Statistics and Probability
237.
Random student is a woman, P(W) = 0.60
Random student is a man, P(M) = 0.40
Random student is born abroad, P(Z)
Women and born abroad, P(Z | W) = 0.01
Men and born abroad, P(Z | M) = 0.04
We have to find: P(W | Z)
Using conditional probability:
Using total law of probability
P(Z) = P(W).P(Z | W) + P(M).P(Z | M) = (0.60 x 0.01) + (0.40 x
0.04) = 0.022
238.
Politician is corrupt, P(C) = 0.80
Politician is honest, P(H) = 0.20
Politician is competent, P(N)
Politician is incompetent, P(Nc)
Given: P(Nc | C) = 0.90
P(N | C) = 1 - P(Nc | C) = 0.10
P(N | H) = 0.65
A)
We have to find: P(H | N)
Using conditional probability:
Using total law of probability:
P(N) = P(C).P(N | C) + P(H).P(N | H) = (0.80 x 0.10) + (0.20 x
0.65) = 0.21
i.e 62% of the competent politicians are honest.
B)
We have to find: P(C | Nc)
P(Nc) = 1-P(N) = 1 - 0.21 = 0.79
Probability that a politician is corrupt if he is incompetent is
0.91