Suppose that in any randomlyselected three pages in our text

Suppose that in any randomly-selected three pages in our textbook, there will be one typographical error. If the number of typos on a given single page is a Poisson random variable, what is the probability of at least one typo on a randomly-selected page? [Hint: instead of time, we use extent of space, but it is the same: think of flipping through the pages one per second, then this is saying that you will see one typo in every three second time period. Figure out the average number of typos per second, or per page....]

Solution

As there are 1 typo in 3 pages, there there are 1/3 = 0.333333333 typos in a page.

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 =    0.333333333      
          
x = the number of successes =    1      
          
Thus, the probability is          
          
P (    1   ) =    0.23884377 [ANSWER]