GATE2014 AG: GA-4

Question

In any given year, the probability of an earthquake greater than Magnitude $6$ occurring in the Garhwal Himalayas is $0.04$. The average time between successive occurrences of such earthquakes is ____ years.

Comments

I have one doubt in the provided solution. Just taking  a small example  to explain my approach.

For example ->  let us say 2 earth quake occur in 4 years then various possibilities are

(1,2)  (1,3)  (1,4)   

         (2,3)  (2,4)

                  (3,4)

where (x, y) means first and second earth quake occurs on year x, y respectively. Above table is representing all possibilities.

Total 6 possibility and sum of time between successive earth quake is (1+2+3   +   1+2   +   1) = 10

So average time between two earth quake is 10/6  = 1.6

But answer will come 2 if method mentioned in various answer is used. So where am i doing mistake ?

---

@Chhotu

I think your approach will give ..Average time between  any two earthquakes 

But here we are asked average time in any two successive earthquakes

Answer 1

Probability of an earthquake greater than magnitude $6$ is $0.04.$

This means $4$ out of $100$ years will face an earthquake greater than magnitude $6.$ So average time between successive earthquakes will be $100/4=25$ years.

Answer 2

Let X

be the number of years to the next earthquake. Then X is a geometric random variable and the

probability that the next earthquake happens in k years is

P(X=k)=(1−p)k⋅p

where p=0.04

.The expected value of X is

E(X)=1/p=1/0.04=25years

Reference:https://math.stackexchange.com/questions/1745059/average-time-between-successive-occurrences-of-earthquakes

Answer 3

Probability of earthquake greater than 6 in a given year=0.04

Average time between two successive earthquakes=when the probability of earthquake becomes 1

i.e 1/(0.04)=25 years

Answer 4

25 years

Comments

cna u pls elaborate!!!!