Question

Forestland Insurance Company underwrites insurance for properties in high density forest areas. It uses the estimate that the probability of a major forest fire destroying a home in any one year is 0.000043. If a homeowner takes a 30-year mortgage on a recently purchased property, what is the likelihood that the owner will experience at least one major forest fire during the mortgage period?

Answer 1

As there are fixed number of trials and probability of success for each and every trial is same and independent of each other, we can use binomial formula

Here we need to use the binomial formula

P(r) = ncr*(p^r)*(1-p)^n-r

Ncr = n!/(r!*(n-r)!)

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial = 0.000043

N = number of trials = 30

R = desired success = at least 1

We know that sum of all the probabilities is = 1

So, p(at least 1) = 1 - p(0)

After substitution

Required probability is = 0.00128919600