Earthquakes along an active fault of length L 200 mi occur

Earthquakes along an active fault (of length L = 200 mi) occur as ruptures of length S.

Compute:

(a.) The conditional probabilities P[E1|S=0.15] and P[E1|S=0.25L]

(b.) The conditional probability P[E1]

(c.) If an earthquake along the fault with the center of the fault rupture within 50 miles of the structure, what is the probability that the length of the rupture was 0.15L and 0.25L, respectively?

Solution

A)

P(E/S=0.15L) = 0.15/0.35 = 0.4286

P(E/S=0.25L) = 0.25 / 0.65 = 0.3846

b)

P(E) = 0.3846+ 0.4286 = 0.8132

c)

for 0.15L

0.35/0.6 = 0.5833

for 0.25L

0.6 / 0.65 =0.9231