Question

Management at a local company asked employees if they were interested in obtaining job training. Responses are summarized by employment type (salaried or hourly), and whether the employee is interested (yes or no) in job training.

Salaried Hourly Total
Yes 49 24 73
No 60 45 105
Total 109 69 178

Required:
a. Compute the probability that an employee is salaried. Give your answer as a decimal, precise to at least three decimal places.
b. Compute the probability that an employee who is interested in training is salaried. Gives your answer as a decimal, precise to at least three decimal places.

Finally, use the results from the two preceding calculations to determine whether or not employment type and interest in training are independent.
a. NO, the two events are not independent.
b. Yes, the two events are independent.

Answer 1

a. P(Salaried)= 0.61

b. P(Salaried/Yes)= 0.68

c. Option: a. NO, the two events are not independent.

Explanation:

Hello!

The table shows information about the employment type and whether the employee is interested in job training. The total sample of employees is 178.

a.

You have to calculate the probability of the employee being Salaried, this is the probability of one of the margins of the table. You can calculate it as the total of employes that are salaried divided by the total of employes surveyed:

P(Salaried)= 109/178= 0.61

b.

Now you have to calculate the probability that the employee is salaried given that he is interested in job training. This is a conditional probability and you can calculate it as:

P(Salaried/Yes)= P(Yes ∩ Salaried) = 0.28 = 0.68

P(Yes) 0.41

To calculate P(Yes ∩ Salaried) you have to divide the number of employees that met both characteristics by the total of employees surveyed: P(Yes ∩ Salaried)= 49/178= 0.275 ≅ 0.28

And to calculate the probability of the employees being interested in job training you have to divide all of them that showed interest by the total pf employees surveyed:

P(Yes)= 73/ 178= 0.41

c.

Remember: Two events are independent when the occurrence of the first one doesn't modify the probability of occurrence of the second one.

If the events "Salaried" and "interested in job training" are independent, then:

P(Salaried/Yes)= P(Salaried)

As you can see

P(Salaried/Yes)= 0.68

P(Salaried)= 0.61

P(Salaried/Yes) ≠ P(Salaried)

Then both events are not independent.

I hope it helps!