Exam 1

Processing math: 100%

Exam 1

Question

An industry-leading company seeks a qualified candidate for a management position. A management consultancy carries out an assessment center which concludes in making a positive or negative recommendation for each candidate: From previous assessments they know that of those candidates that are actually eligible for the position (event

$E$ )

$66 %$ get a positive recommendation (event

$R$ ). However, out of those candidates that are not eligible

$65 %$ get a negative recommendation. Overall, they know that only

$9 %$ of all job applicants are actually eligible.

What is the corresponding fourfold table of the joint probabilities? (Specify all entries in percent.)

$P (E \cap R)$
$P (\overline{E} \cap R)$
$P (E \cap \overline{R})$
$P (\overline{E} \cap \overline{R})$

Solution

Using the information from the text, we can directly calculate the following joint probabilities:

$\begin{matrix} P (E \cap R) & = & P (R | E) \cdot P (E) = 0.66 \cdot 0.09 = 0.0594 = 5.94 % \\ P (\overline{E} \cap \overline{R}) & = & P (\overline{R} | \overline{E}) \cdot P (\overline{E}) = 0.65 \cdot 0.91 = 0.5915 = 59.15 % . \end{matrix}$

The remaining probabilities can then be found by calculating sums and differences in the fourfold table:

	$R$	$\overline{R}$	sum
$E$	5.94	3.06	9.00
$\overline{E}$	31.85	59.15	91.00
sum	37.79	62.21	100.00

$P (E \cap R) = 5.94 %$
$P (\overline{E} \cap R) = 31.85 %$
$P (E \cap \overline{R}) = 3.06 %$
$P (\overline{E} \cap \overline{R}) = 59.15 %$