Final answer:
The question does not provide sufficient data regarding specific investments to determine what we are willing to invest in for the long-term. The concepts mentioned relate to expected value, safety, and risk in investments, all of which are relevant to making investment decisions in the field of probability and statistics.
Step-by-step explanation:
Upon reviewing the provided information, it seems that the question doesn't give us enough context to conclusively determine what long-term investments we are willing to make. Instead, the provided data points such as departure time of a commuter train at rush hour, distance from your house to school, and weight of a bag of rice at the store pertain to statistical understanding, possibly related to calculating expected values, assessing risk, and understanding variability in data.
To answer such a question in probability and statistics, expected value is a key metric that would be calculated for each investment option to determine its profitability. Safety in investments is often evaluated based on the variability or volatility of returns, where lower variability suggests higher safety. Conversely, the riskiest investments are usually those with high variability or uncertainty in their returns. The investment with the highest expected return, on average, would be considered the most profitable, assuming the investor is comfortable with the associated risk level.