1 3 pts the probability that a bridge survives in case of a...

1) (3 pts) The probability that a bridge survives in case of a severe earthquake is 0.4. If 15 bridges are in a region with the occurrence of a severe earthquake, what is the probability that (a) at least 10 survive, (b) from 3 to 8 survive, and (c) exactly 5 survive? Hint: Discrete distribution - binomial dist. (dbinom

Transcript

00:01 Here we are told that strong earthquakes occur according to a plesson process with the mean rate of once in 35 years.

00:09 So if we define a variable x as the number of earthquakes in a given duration, it's distributed according to a plesson distribution with an average rate of 1 over 35 per year.

00:26 And for part a, we were asked for the probability of at most two strong earthquakes occurring within the, next 15 years.

00:38 Now first, the probability mass function for a poisson random variable is given by this formula.

01:00 Now we're considering a 15 year period.

01:04 So we defined the average rate per year, so one year is our basic time unit.

01:11 So for part a, 15 years is t is 15, and so lambda times t is 15 over 35 or 3 over 7.

01:28 We want the probability of at most two earthquakes in this time, so this is the probability that x is less than equal to 2, and this is the probability that x equals 0 plus the probability that x equals 1 plus the probability that x equals 2.

01:46 So using the probability mass function for x equals 0, it simplifies to e to the minus 3 over 7, and then for x equals 1, it's 3 over 7 times e to the minus 3 over 7.

02:05 And then for x equals 2, it's 3 over 7 squared times e to the minus 3 over 7 over 2 factorial.

02:20 And this comes out to approximately 0 .9995.

02:26 And then for part b, we were asked that during a strong earthquake, what is the probability that exactly one of the three bridges collapse? now we are told that the probability that an individual bridge will collapse during a strong earthquake is 0 .25...

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