A destructive earthquake happens once per year.
The exponential equation would be f(x) = 1-e^-x
The probability of going 3 months out of a year would be
P(X≥3/12) ( divide 3 months by 12 months per year).
Now x equals 3/12
Now you have
P = 1-(1-e^-3/12)
= e^-1/4
= 0.7788
The probability that at least 3 months elapse would be 0.7788
(Round answer as needed).
The probability that at least 3 months elapse before the first earthquake of destructive magnitude occurs is; 0.7788
We are told that a destructive earthquake happens once per year.
Thus, the exponential equation in this scenario is;
f(x) = 1 - e⁻ˣ
Thus, the probability that at least 3 months elapse before the first earthquake of destructive magnitude occurs is given as;
P(X ≥ ³/₁₂) since 12 months make a year
This will be;
P(X ≥ ³/₁₂) = 1 - (1 - e^(⁻³/₁₂))
P(X ≥ ³/₁₂) = e^-1/4
P(X ≥ ³/₁₂)= 0.7788
In conclusion, the probability that at least 3 months elapse would be 0.7788
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