Question

uestions 2, 3 and 4 relate to the following information.

The administrative employees of Wyer Co Pty Ltd, can be classified according to the following table:

Salary Level p.a.

Branch

$20,000 - $30,000

$30,001 - $40,000

Albury

3,000

200

Bathurst

1,000

1,600

Wagga

900

2,100

2 The probability that an employee, selected at random, works at the Wagga branch is approximately:

A. 0.71

B. 0.54

C. 0.34

D. 0.18

3 The joint probability that an employee, selected at random, earns $30,001 - $40,000 and works at the Albury branch is approximately:

A. 0.80

B. 0.16

C. 0.05

D. none of the above.

4 The probability that an employee, selected at random, earns between $20,000 and $30,000, given that they work at the Wagga branch, would be an example of a:

A. marginal probability

B. probability that must be calculated in accordance with addition theorem

C. conditional probability

D. joint probability

Answer 1

Salary Level	Albury	Bathurst	Wagga	Total
$20,000 - $30,000	3,000	1,000	900	4,900
$30,001 - $40,000	200	1,600	2,100	3,900
	3,200	2,600	3,000	8,800

Solution to 2.

Probability that an employee, selected at random, works at the Wagga branch

= Total Number of Employee at Wagga Branch / Total Number of Employee = 3,000 / 8,800 = 0.3409

=0.34, So option C. 0.34 is correct

Solution to 3.

Joint Probability = (Probability of Albury Branch) * (Probability of earns $30,001 - $40,000)

= (Employee at Albury / Total Employee) * (Employee earns $30,001 - $40,000 / Total Employees)

= (3200 / 8800) * (3900 / 8800) = (0.3636) * (0.4431) = 0.1611

= 0.16, So option B. 0.16 is correct

Solution to 4.

Option C. is correct

This is the conditional probability where probability will be calculated on the condition of  employee work at the Wagga branch.