A seismologist models earthquake probability and finds that a certain fault has a 3% chance of producing a major quake each year. Assuming independence, what is the probability (in percent) that no major quake occurs in the next 10 years?

["Understanding Earthquake Risk: Calculating the Odds of No Major Quake in 10 Years", "When it comes to earthquake preparedness, understanding the likelihood of a major seismic event is crucial. A recent analysis by a leading seismologist reveals that a specific fault has a 3% annual probability of producing a major earthquake—defined as a quake strong enough to cause significant damage. But what does this mean probabilistically over time?", "### The Annual Risk: A 3% Chance of a Major Quake", "Each year, the probability of a major quake occurring is 3%, or 0.03. If the events are independent year to year—meaning one year’s quake has no effect on the next—the probability of no major quake in a given year is:\n[ 1 - 0.03 = 0.97 ]\nor 97%.", "### Calculating the 10-Year Probability", "To find the chance of no major earthquake occurring over the next 10 consecutive years, we raise the yearly non-occurrence probability to the 10th power:\n[ (0.97)^{10} ]", "Using precise calculation:\n[ (0.97)^{10} \approx 0.7374 ]", "Converting this to a percentage:\n[ 0.7374 \ imes 100 = 73.74% ]", "### Interpretation: Nearly a 73-to-1 Ratio Against a Major Quake in the Next Decade", "This means there is approximately a 73.7% probability that no major earthquake will occur in the next 10 years—over a 73% chance that the fault will remain quiet despite having a 3% annual risk. While this reflects relatively low annual risk, seismic hazards are inherently probabilistic and long-term, so such extended timeframes reduce the immediate likelihood significantly—at least on paper.", "### Why This Matters for Preparedness", "While the odds suggest a favorable short-term outlook, the 3% yearly risk adds up over time. Earthquake models emphasize that even small annual probabilities accumulate, making proactive disaster planning essential. From retrofitting buildings to establishing emergency protocols, understanding these probabilities helps communities prepare and reduce potential losses.", "---", "In summary: Assuming independence, there is approximately 73.7% chance that no major earthquake will occur along the fault over the next 10 years, highlighting the importance of sustained preparedness even when risk appears moderate annually."]