Question

Asked Feb 25, 2019

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Department | |||

Sex | Packaging | shipping | total |

Female | 32 | 48 | 80 |

male | 48 | 72 | 120 |

Total | 80 | 120 | 200 |

A local mail-order catalog business employs 200 people in the packaging and shipping departments. The personnel department maintains the records shown in Table below. Questions have arisen whether there has been a tendency to place female workers in the packaging department instead of in the shipping department. Management feels that there is no relationship between being female and working in the packaging department. They feel that these two events are independent. If an employee is selected at random from the 200 total employees, what is the probability that the employee works for the packaging department? A) if the employee selected at random is male, what is the probability that he works for the shipping department? B) if the employee selected at random is male, what is the probability that he works for the packaging department? C) is the probability of being male independent?

Step 1

Given data of 200 male and female employees in packaging and shipping departments shown below.

The events being female and working in packaging department are independent events.

Given that employee selected at random is male and we need to calculate the probability that he works in shipping department.

Let event M be selecting male employee and event S be working in Shipping department. So here we need P(S | M)

Total employees = 200

total males = 120

P(M) = 120/200

Total males and working in shipping department = 72

Total employees = 200

P(S ∩ M) = 72/200

Using formula of conditional probability as shown below we get P(S | M) = 0.60

Step 2

Given the employee selected is male and we need to find the probability that he works in packaging deparment. Let event M be that a selected employee works in packaging department. So we need P(P | M).

P(M) = 120/200

Total n...

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