An Examination for a certain skill was given to 100 employee

An Examination for a certain skill was given to 100 employees of a firm. Forty of the employees were male. Sixty of the employees passed the examination. Twenty-four of the males passed the test.

A) Construct a joint probability table for the 100 employees.

B) Find the probability that the employee passed, given that he was a male.

C) Find the probability that the employee was male, given the he passed.

D) Are the events pass and female independent? Why or Why not?

E) Are the events pass and female mutually exclusive? Why or Why not?

Solution

a)

   Male   Female   Total
Passed   24   36   60
Failed   16   24   40
Total   40   60   100

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b)

from the table,

P(passed/male) = [24 passed males]/40 males = 0.60 [answer]

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c)

P(male|passed) = [24 passed males]/60 passed = 0.40 [answer]

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d)

If they are indepedent, they P(pass|female) = P(pass).

P(pass|female) = [36 passed females]/60 females = 0.60
P(pass) = 0.60

Thus, YES, THEY ARE INDEPENDENT.

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E.

If they are mutually exclusive, they no female should pass.

As 36 females passed, NO, THEY ARE NO MUTUALLY EXCLUSIVE. [ANSWER]