Analyzing Decisions and Strategies with Probability Practice Test

A city is planning snow response for a weekend. Forecast data for the region:

• $20%$ chance of heavy snow
• $50%$ chance of light snow
• $30%$ chance of no snow

If the city pre-treats roads Friday night, it reduces the chance of major traffic disruption to:

• $15%$ if heavy snow occurs
• $5%$ if light snow occurs
• $1%$ if no snow occurs

If the city does not pre-treat, the chance of major traffic disruption is:

• $40%$ if heavy snow occurs
• $12%$ if light snow occurs
• $1%$ if no snow occurs

The city’s goal is to minimize the overall probability of major traffic disruption. Which strategy is most reasonable given the probabilities?

A retailer is deciding how to handle an online fraud alert system. About $1%$ of orders are truly fraudulent.

Option A (Aggressive): flags $95%$ of fraudulent orders, but also flags $10%$ of legitimate orders.

Option B (Conservative): flags $75%$ of fraudulent orders, but flags only $2%$ of legitimate orders.

Flagged orders are delayed for verification, which harms customer experience. The retailer’s goal is to keep the fraction of all orders that get delayed as low as possible while still catching at least $70%$ of fraudulent orders. Which strategy is most reasonable given the probabilities?