geometric distribution Drivers are not permitted to turn rig

Drivers are not permitted to turn right on red from 7am to 7pm at a particular junction. Having known that 1 out of 11 drivers default, the police is strategically positioned to catch defaulters. Find the probability that the first defaulter was found before 8 drivers were observed.

Solution

Note that for a geometric distirbution,

P(x) = p (1-p)^(x-1)

where x = the amount of trials before the first success

p = the probability of success = 1/11

Now, consider the table:

Thus, adding all the entries in the P(X) column,

P(before 8) = P(at most 7) = 0.486841882 [answer]

x	P(x)
1	0.090909
2	0.082645
3	0.075131
4	0.068301
5	0.062092
6	0.056447
7	0.051316
Total	0.486842