Question

Under 2 miles 2–4 miles 5–6 miles Over 6 miles
Car 15 25 30 40
Public Transit 20 20 35 15
Bike 30 15 10 5
Walk 25 10 5 0
Part A: Calculate the empirical conditional probability of an employee who takes public transit to work, given that they live over 6 miles away. Show all work. (2 points)

Part B: Is an employee more or less likely to take public transit if they live over 6 miles away? Justify the answer mathematically. (2 points)

Answer 1

Part A:

To calculate the empirical conditional probability of an employee who takes public transit to work, given that they live over 6 miles away, we need to use the formula:

P(Takes public transit | Lives over 6 miles away) = P(Takes public transit and Lives over 6 miles away) / P(Lives over 6 miles away)

From the table, we can see that the number of employees who take public transit and live over 6 miles away is 15.

The total number of employees who live over 6 miles away is 40 + 15 + 5 + 0 = 60.

Therefore, the probability of an employee who takes public transit to work, given that they live over 6 miles away is:

P(Takes public transit | Lives over 6 miles away) = 15 / 60 = 0.25 or 25%.

Answer 2

Part B:

To determine whether an employee is more or less likely to take public transit if they live over 6 miles away, we can compare the probability of taking public transit for employees who live over 6 miles away with the overall probability of taking public transit.

The overall probability of taking public transit is:

P(Takes public transit) = (20 + 20 + 35 + 15) / (15 + 25 + 30 + 40) = 0.375 or 37.5%.

The probability of taking public transit for employees who live over 6 miles away is:

P(Takes public transit | Lives over 6 miles away) = 15 / 60 = 0.25 or 25%.

Comparing the two probabilities, we can see that an employee is less likely to take public transit if they live over 6 miles away. This is because the probability of taking public transit for employees who live over 6 miles away is lower than the overall probability of taking public transit.

Answer 3

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Answer 4

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