In a city district of 10 by 10 blocks there are 400 people w

In a city district of 10 by 10 blocks there are 400 people with flu. What is the probability that none of these people live in your block, assuming that they are randomly distributed in the district?

Solution

There are 100 blocks. Thus, on the average, there are 400/100 = 4 people with flu per block.

By Poisson distirbution, note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    4      
          
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.018315639 [ANSWER]