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Chapter 4: Problem 91

The probability that an employee at a company is a female is .36. The probability that an employee is a female and married is .19. Find the conditional probability that a randomly selected employee from this company is married given that she is a female.

Short Answer

Expert verified
The conditional probability that a randomly selected employee from this company is married given that she is a female is approximately 0.5277.

Step by step solution

01

Understand the variables and formula

We have the following variables and formula: The probability that an employee is a female, P(F) = 0.36. The probability that an employee is a female and married, P(F 鈭� M) = 0.19. The formula for conditional probability is P(A|B) = P(A 鈭� B) / P(B). In our case, A is the event that the employee is married, and B is the event that the employee is a female.
02

Substitute the known values into the formula

Substitute the known values into the formula as follows: P(M|F) = P(F 鈭� M) / P(F). Substitute the known values: P(M|F) = 0.19 / 0.36.
03

Calculate the result

Carrying out the division operation gives P(M|F) = 0.19 / 0.36 = 0.5277 approximately. Hence, the conditional probability that a randomly selected employee from this company is married given that she is a female is around 0.5277.

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Most popular questions from this chapter

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