Earthquake Average Time Calculation
The problem asks for the average time between successive earthquakes greater than Magnitude 6 in the Garhwal Himalayas, given the annual probability.
Given Probability
- Probability ($P$) of an earthquake > Magnitude 6 occurring in a year = 0.04
Calculating Average Time Between Events
For events that occur randomly over time at a constant average rate (like earthquakes in this model), the average time between successive events is the reciprocal of the probability (or rate) per unit time.
The formula is:
Average Time = $ \frac{1}{P} $
Calculation
Substitute the given probability into the formula:
Average Time = $ \frac{1}{0.04} $
Average Time = $ \frac{1}{\frac{4}{100}} $
Average Time = $ \frac{100}{4} $
Average Time = 25 years
Conclusion
The average time between successive occurrences of earthquakes greater than Magnitude 6 in the Garhwal Himalayas is 25 years.
Important Questions from Probability
Three dice are thrown. What is the probability of getting a sum which is a perfect square?
Two distinct natural numbers from 1 to 9 are picked at random. What is the probability that their product has 1 in its unit place?
Two dice are thrown. What is the probability that difference of numbers on them is 2 or 3 ?
Suppose that there is a chance for a newly constructed building to collapse, whether the design is faulty or not. The chance that the design is faulty is 10%. The chance that the building collapses is 95% if the design is faulty, otherwise it is 45%. If it is seen that the building has collapsed, then what is the probability that it is due to faulty design?
What is the probability that all three boys sit together?
