We want to find which route should we use. To do so, we will calculate conditional probability of being on time for every route.
Making a Two-Way Table of Frequency Counts
First we will use the given table of records 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 the total sum of all records, which is 41.
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 being on time for every route. Let's remember the formula for the conditional probability.
P(B|A)=P(AandB)/P(A)
The event B in the formula is being on time, and event A is choosing the route A. We will divide joint relative frequency from the column On Time by the marginal frequency in the corresponding row to get the conditional probability for every route. We will start with Route A.
