2. Fifty percent of the employees in a utility company are male. Fifty percent o

Question

2. Fifty percent of the employees in a utility company are male. Fifty percent of the employes cam more tha 30K a year. Twenty-five percent of the employces are male and carn more than S30K a year a. If an employee is taken at random, what is the probability that the employee is male? b If an employee is taken at random, what is the probability that the cmployee ears more than $30k If an employee is taken at random, what is the probability that the employee is male and eamis more S30K a year? c. d. Ifan employee is taken at random, what is the probablity thst the employee is nale or canus more tha S30K a year? he earns more than e. The employee taken at random turns out to be male Compute the probability that he 30K a year

Explanation / Answer

Here we are given that 50% of the emplyees are male, therefore P(male ) = 0.5

Also earnings more than 30K probability is 0.5. Therefore P( earn more ) = 0.5

Also we are given that P( male and earn more ) = 0.25

a) This is already given to us. If an employee is selected at random, the probability that it is a male is given as: P(male ) = 0.5

b) This is already given to us. If an employee is selected at random, the probability that he earns more than 30K is given as: P(earn more ) = 0.5

c) This is already given to us. If an employee is selected at random, the probability that he is male and he earns more than 30K is given as: P(male and earn more ) = 0.25

d) Using addition law of probability we get:

P( male or earn more) = P(male ) + P( earn more ) - P( male and earn more ) = 0.5 + 0.5 - 0.25 = 0.75

Therefore the required probability here is 0.75

e) Given that the employee is male, probability that he earns more than $30 K is computed using the Bayes theorem as:

P( earn more | male ) = P( male and earn more ) / P( male ) = 0.25 / 0.5 = 0.5

Therefore 0.5 is the required probability here.

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.