Question

In: Statistics and Probability

237. In a university it was observed that 1% of women and 4% of men enrolled...

237. In a university it was observed that 1% of women and 4% of men enrolled were born abroad. There is also the fact that 60% of the total student population of that institution are women. If the file of a student reports that he was born in another country, what is the probability that it is a woman?


238. - if we argue that 80% of politicians in a certain country are corrupt and 20% are honest; and also, among those who are corrupt, 90% are incompetent, while the honest, 65% are competent:
A) What percentage of the competent politicians of that place are honest?
B) What is the probability that a politician is corrupt if his actions show that he is incompetent?

Solutions

Expert Solution

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


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