Question

100 years of history shows that an isolated forest in Europe, containing over one million trees, there is a .10 % chance that one tree will be uprooted by windstorms in the month of March of any given year. What is the probability that three trees will be uprooted next March? Show all work and method used.

Answer 1

*Answer) As there is .10% chance that one tree will be uprooted by windstorms in the month of March of any given year

so the probability(one tree uprooted) = 0.001

therefore p = 0.001 and q = 1-0.001 = 0.999

here we will use binomial to find the probability that three trees will be uprooted next March

ⁿc_r *p^rq^n-r   , n = 3 and r = 1

³c₁*0.001¹*0.999^3-1

= (3!/1!(3-1)! )*0.001*0.999²

= (3*2*1/2*1)*0.001*0.999² (ⁿc_r= n!/r!(n-r)!)

= 0.002994003

= 0.003 (approx)