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Arada [10]
3 years ago
5

California is hit every year by approximately 500 earthquakes that are large enough to be felt. However, those of destructive ma

gnitude occur, on average, once a year. Find a) Probability that at least 3 months elapse before the first earthquake of destructive magnitude occurs. b) Probability that at least 7 months elapsed before the first earthquake of destructive magnitude occurs knowing that 3 months have already elapsed.
Expert Answer
Mathematics
1 answer:
Elanso [62]3 years ago
8 0

Answer:

a) The probability that at least 3 months elapse before the first earthquake of destructive magnitude occurs is P=0.7788

b) The probability that at least 7 months elapsed before the first earthquake of destructive magnitude occurs knowing that 3 months have already elapsed is P=0.7165

Step-by-step explanation:

Tha most appropiate distribution to model the probability of this events is the exponential distribution.

The cumulative distribution function of the exponential distribution is given by:

P(t

The destructive earthquakes happen in average once a year. This can be expressed by the parameter λ=1/year.

We can express the probability of having a 3 month period (t=3/12=0.25) without destructive earthquakes as:

P(t>0.25)=1-P(t

Applying the memory-less property of the exponential distribution, in which the past events don't affect the future probabilities, the probability of having at least 7 months (t=0.58)  elapsed before the first earthquake given that 3 months have already elapsed, is the same as the probability of having 4 months elapsed before an earthquake.

P(t>0.58)/P(t>0.25)=P(t>0.33)

P(t>0.33)=1-P(t

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