The probability of a tornado occurring in a county in US has

The probability of a tornado occurring in a county in US has been estimated to be 0.15 for one
occurrence, 0.07 for two occurrence, 0.05 for three occurrences, and 0.009 for four occurrences during
the next 10 years. Assume the chances of five or more occurrences happening during the next ten
years is zero. If a tornado hits, the probability that a neighborhood in the county is damaged is
0.70. Assume that the damage from multiple tornados is independent. What is the probability that
the neighborhood will not suffer any damage from tornados in the next 10 years?

Solution

HEre we apply the concept of total probability .

So the probability of being damage = probability of first occurrence x( probability of first occurrence x probability of neighbourhood country, not damaging +probability of second occurrence x probability of neighbourhood country, not damaging +probability of third occurrence x probability of neighbourhood country, not damaging + probability in fourth occurrence x probability of not damagin)

=0.15 ( 0.15 x (1-0.7) + 0.07 x 0.3 + 0.05 x 0.3+0.009 x 0.3)

= 0.15 ( 0.045+ 0.021 +0.015+0.0027)

=0.15 x 0.0837 = 0.012555

So required probability of not damagin = 1 - 0.012555 = 0.987

Answer