Probability of flood.

Question

I was solving a question of probability and the question was " If the probability of occurrence of flood in any year is 1/20 then what is probability that flood will occur in 3rd year exactly? This is easy to solve and the answer that I got is 361/8000. But then one question strikes my mind what if exactly is not written? What if we need to find the probability that flood will occur in 3rd year? On the previous question my approach was 19/20 × 19/20 × 1/20. But I am sure that this can not be applied to latter question. I think this will be solved by probability distribution however I am not sure about this. If anyone know how to solve this please provide guidance.

Answer 1

In any year the probability is $\frac1{20}$, so also for the $3$rd year.

Answer 2

First of all, in your previous computation your approach is correct but the result is wrong: $$19/20 \cdot 19/20 \cdot 1/20=\frac{361}{8000}.$$ As regards your variation, if you would like to evaluate the probability that the flood occurs within the third year, i.e. the first year or the second year or the third year, then it should be: $$1/20+(19/20\cdot 1/20)+(19/20 \cdot 19/20 \cdot 1/20)=\frac{1141}{8000}.$$ Note that the probability that the flood occurs the third year (we remove the word "exactly"), or any other year, is just $1/20$.