1. A blaster rifle manufacturing facility on Naboo has 6,000 employees. The empl

Question

1. A blaster rifle manufacturing facility on Naboo 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 gender. Reduce all fractions and express your answers as a percentage.

.....................Male.........Female........Total

Four days......300.............600........... 900

Five days...... 1,200........ 1,500..........2,700

Flexible...........300.......... 2,100......... 2,400

Total..............1,800......... 4,200..........6,000

a. What is the probability that a randomly selected employee is a woman and is in favor of a four-day work week?

b. What is the probability that a randomly selected employee is male?

c. A randomly selected employee turns out to be male. Compute the probability that given the employee is a male, he is in favor of flexible hours.

d. What percentage of employees are in favor of a four-day work week?

e. Given that a person is in favor of flexible time, what is the probability that the person is a male?

Explanation / Answer

(a) P(event) = No. of favourable outcomes/Total Outcomes

Favourable: Woman and in favour of a 4 day week = 600 and Total Outcomes = 6000

Therefore Probability = 600/6000 = 1/10 = 0.1 = 10%

(b) Probability ( Male)

Favourable: No of Males = 1800, and Total Outcomes = 6000

P(Male) = 1800/6000 = 3/10 = 0.3 = 30%.

(c) P(Favour of flexible hours given he is a male) = P(Flexible hours/Male) = P(Flexible hours and Male)/P(Male)

P(Flexible Hours and Male) = 300/6000 and P(Male) = 1800/6000

Therefore P(Flexible hours/Male) = (300/6000) / (1800/6000) = 300/1800 = 1/6 = 0.1667 = 16.67%

(d) Employees in favour of a 4 day week = 900

Therefore % of employees in favour of a 4 day week = (900/6000) * 100 = 15%

(e) P(Of a male given that the person is in favour of flexible time) = P(Male/Favour of Flexible time)

= P(Male and Flexible Time)/P(Flexible Time);

P(Flexible Time) = 2400/6000 and P(Male and Flexible Time) = 300/6000

Therefore P(Male/Favour of Flexible time) = (300/6000) / (2400/6000) = 300/2400 = 1/8 = 0.125 = 12.5%

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