Make a two-way table of relative frequencies. Then calculate the conditional probability of completing tasks above the expectations for every employee.
Sam, see solution.
Practice makes perfect
We will find which of the employees should be offered the promotion. To do so, we will calculate the conditional probability of completing tasks above the expectations for every employee.
Making a Two-Way Table of Frequency Counts
First we will use the given table of records made by the manager to make a two-way table of frequency counts. If we count the segments and write the results as numbers, we will get a table that shows the joint frequencies.
To calculate the marginal frequencies we will sum the values in columns and rows.
Now we know the marginal frequencies and the total sum of all tasks, which is 53.
Let's evaluate these expressions and round the results to the nearest hundredths.
Calculating the Conditional Probabilities
Finally, we will find the conditional probability of completing tasks and exceeding the expectations for every employee. Let's remember the formula for the conditional probability.
P(B|A)=P(AandB)/P(A)
The event B in the formula is completing the task above the expectations, and event A is choosing the employee A for the task. We will divide joint relative frequency from the column Exceed Expectations by the marginal frequency in the corresponding row to get the conditional probability for every employee. We will start with Joy.
Basing on the sample, we obtained that Sam has the greatest probability of completing tasks while exceeding the expectations. Therefore, the manager should choose Sam for the promotion.
