Need a hint on how to approach the problem

A

Alex Ouroumidis

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In a region of Japan the frequency of occurrence of a strong earthquake is six times lower than the occurrence of a moderate earthquake, which in turn has a frequency of occurrence which is three times lower than the occurrence of a low-intensity earthquake. The probability of irreparable building damage (broken column or beam) is 0.08, 0.28 and 0.44.
A. What is the probability that the next earthquake will be of strong intensity?
B. What is the probability that in the next earthquake we will have irreparable damage to the buildings
C. In the event that two earthquakes occur within a limited period of time, what is the probability that there will be no irreparable damage to the buildings?I
I'm having trouble understanding what type of problem this is.
Should I define a random variable and name strong,moderate,low-intensity (1,2,3) then somehow find the probability P(X=1), P(X=2)...? Also, what do I need to read up on to solve such problems? Any hint is much appreciated . (I'm translating all of this so please excuse any mistakes in terminology.)
 
I suppose that "six times lower" is to be taken as "1/6 as great"; some would consider that an improper term.

I would start by figuring out what the first paragraph is saying, which is not easy. At first I thought we needed more information, until I realized we need only consider the set of all earthquakes. We are told that for each strong earthquake there are 6 moderate earthquakes, and for each of those there are 3 low-intensity quakes. So we have a ratio of 1:6:18.

From that, what is your answer to (a)?
 
In case you are like me and try to avoid expressing things in terms of ratios and rely on algebra:

[MATH]p_S + p_M + p_L = 1[/MATH] where the variables

represent the probabilities of strong, moderate, and low intensity earthquakes respectively, you have three unknowns so you need two more equations.
 
Alex Ouroumidis said:
In a region of Japan the frequency of occurrence of a strong earthquake is six times lower than the occurrence of a moderate earthquake, which in turn has a frequency of occurrence which is three times lower than the occurrence of a low-intensity earthquake. The probability of irreparable building damage (broken column or beam) is 0.08, 0.28 and 0.44.
A. What is the probability that the next earthquake will be of strong intensity?
B. What is the probability that in the next earthquake we will have irreparable damage to the buildings
C. In the event that two earthquakes occur within a limited period of time, what is the probability that there will be no irreparable damage to the buildings?I
I'm having trouble understanding what type of problem this is.
Should I define a random variable and name strong,moderate,low-intensity (1,2,3) then somehow find the probability P(X=1), P(X=2)...? Also, what do I need to read up on to solve such problems? Any hint is much appreciated . (I'm translating all of this so please excuse any mistakes in terminology.)
Click to expand...
Let "x" be the probability a given earthquake is "strong". Then the probabity the earthquake is "moderate" is 6x and the probability the earthquake is "low" is 3(6x)= 18x.

Since any earthquake is one of those categories, x+ 6x+ 18x= 25x= 1 so x= 1/25= 0.04. The probability an earthquake is "strong" is 0.04, "moderate" is 6(0.04)= 0.24, and "low" is 3(0.24)= 0.72.

That gives you (a). For (b), the probability there will be "irreperable damage" is 0.08(0.72)+ 0.28(0.24)+ 0.44(0.04).

For any one earthquake, the probability there will be NO "irreprable damage" is 1 minus that. The probability for two consecutive earthquakes is the probability for one earthquake, squared.
 
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