14 A government agency has 6000 employees The employees were

14. A government agency has 6,000 employees. The employees were asked whether they preferred a four-day work week (10 hours per day), a five-day work week (8 hours per day), or flexible hours. You are given information on the employees responses broken down by sex. a. What is the probability that a randomly selected employee is a man and is in favor of a four-day work week? b. What is the probability that a randomly selected employee is female? c. A randomly selected employee turns out to be female. Compute the probability that she is in favor of flexible hours. d. What percentage of employees is in favor of a five-day work week? e. Given that a person is in favor of flexible time, what is the probability that the person is female? f. What percentage of employees is male and in favor of a five-day work week?

Solution

for this exercise we just need the information of the table

a)

man and is in favor of a 4 day work week = 300

total = 6000

Probability = 300/6000 = 0.05

b)

employee is female = 4200

total = 6000

probability = 4200 / 6000 = 0.7

c)

she is in favor of flexible hours = 2100

is female = 4200

probability = 2100 / 4200 = 0.50

d)

in favor of 5 day work week = 2700

total = 6000

probability = 2700 / 6000 = 0.45 = 45%

e)

female and flexible = 2100

flexible = 2400

probability = 2100 / 2400 = 0.875

f)

male and in favor of 5 day work = 1200

total = 6000

probability = 1200 / 6000 = 0.2 = 20%