Probability

Question

The probability that South Florida will be hit by a major hurricane in any single year is 5/19. What is the probability that south Florida will be hit by a major hurricane at least once in the next four years? 

Answer 1

Probability of at least once  is the same is

 

1  -  Probability of NONE at all

 

 

It is binomial,  p=5/19, N=4, k=0, with formula (N choose k)* p^k * (1-p)^(N-k)

 

  So to calculate the probability that it will not happen in four years,

 

  we first note that the first two terms in the formula, namely the

 

  combinatoric (4 choose 0) AND (5/19)^0 are both equal to 1

 

The probability is then (14/19)^4 <--- it will not happen for 4 years in a row

 

= 38416/130321 = 0.294779813....

 

The final answer is then:

91815/130321 = 0.704529585.... or ALMOST 70.5%

 

So chances are we are gonna get hit ;-)