325 About ten percent of users do not close Windows properly

3.25. About ten percent of users do not close Windows properly. Suppose that Windows is installed in a public library that is used by random people in a random order.

(a) On the average, how many users of this computer do not close Windows properly before someone does close it properly?

(b) What is the probability that exactly 8 of the next 10 users will close Windows prop- erly?

Solution

a)

0.10 do not close the windows properly. Thus, 0.90 close the windows properly. Thus, on the average,

k = 1/p(close properly) = 1/0.9 = 1.11111 use it before someone does close it properly.

b)

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    10      
p = the probability of a success =    0.9      
x = the number of successes =    8      
          
Thus, the probability is          
          
P (    8   ) =    0.193710245 [answer]