I knew this was a Bayes setup but fumbled the direction of conditioning for a second.
Clarify the question by defining the population and time frame, then use Bayes' theorem with conditional probabilities estimated from Lyft's data. Discuss how to derive P(took Lyft to work | took Lyft home) using trip history and user segmentation.
Pro tip: Show awareness of data limitations and propose a practical method to estimate the probabilities, such as using historical ride data or A/B testing, rather than just theoretical calculations.
Define what 'took Lyft home' and 'took Lyft to work' mean, including time frames (e.g., same day, typical behavior) and population (e.g., all riders, commuters).
Determine the conditional probability P(To Work | Home) and recognize that it can be computed using Bayes' theorem: P(To Work | Home) = P(Home | To Work) * P(To Work) / P(Home).
Discuss how to estimate each component from Lyft's data: P(To Work) as the overall proportion of riders who take Lyft to work, P(Home) as the proportion who take Lyft home, and P(Home | To Work) as the likelihood of taking Lyft home given they took it to work.
Address potential biases such as selection bias (only observing riders who use Lyft) and confounding factors (e.g., time of day, location, user habits).
Plug in estimated values to compute the probability, and interpret the result in business terms, noting any caveats about data quality and generalizability.
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