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
Two dice are thrown simultaneously and the sum of the numbers appearing on them is noted. What is the probability that the sum is 12?
If a box contains 3 white cushions, 4 red cushions and 5 blue cushions, what is the probability of selecting a white or blue cushion?
A. 2/3
B. 3/4
C. 1/4
D. 1/9Statements followed by some conclusions are given below.
Statements:
1. A bag has 2 white, 3 black, 4 red and 6 green balls.
2. 1 ball selected at random from the bag.
Conclusions:
I. The probability that a black ball is selected is 1/5
II. The probability that a red ball is selected is 6/15
Find which of the conclusions logically follows from the given statement
A. Only conclusion I follows.
B. Only conclusion II follows.
C. Both I and II follow.
D. Neither I nor II follows.
In a shooting test, the probabilities of hitting the target are 1/2 for A, 2/3 for B and 3/4 for C. If they fire at the same target, what is the probability that only one of them hits the target?
A bag contains balls numbered from 1 to 42. One ball is drawn at random from these balls. The probability that its number is a multiple of 7 or 8 is:
