Question

The data tabulated below are for flooding events in the last 400 years. 
The probability of a large flood accompanied by a glacial lake outburst flood (GLOF) in 2025 is ........... \(\times 10^{-3}\). (Round off to one decimal place)
 

Year	Flood Size	Magnitude rank
1625	Large	2
1658	Large + GLOF	1
1692	Small	4
1704	Large	2
1767	Large	2
1806	Small	4
1872	Large + GLOF	1
1909	Large	2
1932	Large	2
1966	Medium	3
2023	Large + GLOF	1

Hint:

To calculate the probability of an event over a certain time period, count the number of occurrences and divide by the total number of events within the time frame.

Answer 1

Step 1: Identifying the events of interest.
From the given table, we focus on the years when a "Large + GLOF" event occurred

Year	Flood Size	Magnitude rank
1625	Large	2
1658	Large + GLOF	1
1692	Small	4
1704	Large	2
1767	Large	2
1806	Small	4
1872	Large + GLOF	1
1909	Large	2
1932	Large	2
1966	Medium	3
2023	Large + GLOF	1

From the table, the "Large + GLOF" events occurred in the years 1658, 1872, and 2023. These are the relevant events to calculate the probability.

Step 2: Total number of events in the last 400 years.
The total number of events from 1625 to 2023 is 11.

Step 3: Number of events with "Large + GLOF".
There are 3 events where "Large + GLOF" occurred (1658, 1872, 2023).

Step 4: Probability calculation.
The probability of a large flood accompanied by a GLOF in 2025 is the ratio of "Large + GLOF" events to the total number of events: \[ P = \frac{\text{Number of "Large + GLOF" events}}{\text{Total number of events}} = \frac{3}{11} \approx 0.2727 \] Step 5: Adjust for the year range.
Since this is over a 400-year period, the probability per year is: \[ P_{\text{yearly}} = \frac{0.2727}{400} \approx 0.000682 \approx 0.7 \times 10^{-3} \] 
Final Answer:
\[ \boxed{0.7 \times 10^{-3}} \]