13 votes 13 votes 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. Quantitative Aptitude gate2014-ag quantitative-aptitude probability numerical-answers normal + – makhdoom ghaya asked Mar 21, 2016 • edited Jun 7, 2018 by Milicevic3306 makhdoom ghaya 4.1k views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply Chhotu commented Oct 18, 2017 i edited by Chhotu Oct 18, 2017 reply Follow Share 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 ? 0 votes 0 votes jatin khachane 1 commented Nov 28, 2018 reply Follow Share @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 0 votes 0 votes Please log in or register to add a comment.
Best answer 24 votes 24 votes 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. Aditya Sharma answered Mar 31, 2016 • selected Apr 7, 2016 by Pooja Palod Aditya Sharma comment Share Follow See all 0 reply Please log in or register to add a comment.
4 votes 4 votes 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 sutanay3 answered Jul 18, 2018 sutanay3 comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes 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 srivivek95 answered Apr 6, 2016 srivivek95 comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes 25 years bad_engineer answered Mar 22, 2016 bad_engineer comment Share Follow See 1 comment See all 1 1 comment reply richa07 commented Mar 30, 2016 reply Follow Share cna u pls elaborate!!!! 0 votes 0 votes Please log in or register to add a comment.