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Answer:
15.24% probability that at least 2 will still stand after 35 years
Step-by-step explanation:
To solve this question, we need to understand the binomial distribution and the exponential distribution.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
In which is the decay parameter.
The probability that x is lower or equal to a is given by:
Which has the following solution:
The probability of finding a value higher than x is:
Probability of a single tower being standing after 35 years:
Single tower, so exponential.
Mean of 25 years, so
We have to find
What is the probability that at least 2 will still stand after 35 years?
Now binomial.
Each tower has a 0.2466 probability of being standing after 35 years, so
3 towers, so
We have to find:
In which
15.24% probability that at least 2 will still stand after 35 years