Make a two-way table of relative frequencies. Then calculate the conditional probability of completing tasks above the expectations for each group.
Group 1, see solution.
Practice makes perfect
We want to find which group should be awarded the prize. To do so, we will calculate the conditional probability of completing tasks above the expectations for every group.
Making a Two-Way Table of Frequency Counts
First we will use the given table of records made by the teacher 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 the columns and rows.
Now we know marginal frequencies and total sum of all tasks, which is 44.
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 the tasks while exceeding the expectations for every group. Let's remember the formula for conditional probability.
P(B|A)=P(AandB)/P(A)
Event B in the formula is completing the task above the expectations, and Event A is choosing Group A for the task. We will divide the joint relative frequency from the column Exceed Expectations by the marginal frequency in the corresponding row to get the conditional probability for every group. We will start with Group 1.
Basing on the sample, we obtained that Group 1 has the greatest probability of completing tasks and exceeding the expectations. Therefore, the teacher should choose Group 1 to be awarded the prize.
