Quick homework question...

[Pat Southern]

I'm getting a probability of over 100% so I figure that's not correct. Part i and ii aren't really important, I just need to show effort, but part iii will be graded.

3. (20) There are two leading models of earthquake predicition, M1 and
M2. According to M1, the annual rate of a major earthquake (Richter scale 7
and above) in California is 1%, and earthquake probabilities are independent
over time {this is a somewhat problematic assumption for earthquakes, since
the energy to be released by an earthquake builds up over time}. According to
the alternative modelM2, the annual rate of a major earthquake in California
is 3%, and, again, earthquakes are independent over time.
M2 is favored by the majority of scientists, so you assign probability 70%
to M2 and 30% to M1.
i) What is the chance of at least one major earthquake in California over
the next 100 years, given that M2 is true?
ii) What is the chance of at least one major earthquake in California over
the next 100 years, given that you do not know which of the two models is
correct.
iii) What is the chance of exactly one earthquake, given that M1 is true?

[AaronBrown]

(i) The probability of at least one is one minus the probability of zero. The probability of zero is 0.97^100.

(ii) The probability of zero is 0.3 x 0.99^100 + 0.7 x 0.97^100. Subtract from one, as in (i).

(iii) The chance of getting exactly one earthquake, and having it in the first year, is 0.01 x 0.99^99. The chance of getting exactly one earthquake in any year is 100 times this number.

[Pat Southern]

Thanks Aaron.