probability to be fined= 0.22
suppose the employee irregularly parks on 7 deliveries, what is probab that is not fined??
Please help now!
Let X be the number of times the employee is not fined, so X is a random variable binomially distributed like this:
$\displaystyle X \sim Bi(n, \theta) $
$\displaystyle X \sim Bi(7, 0.78) $ where 7 is the number of times the "experiment" is repeated, i.e. the number of time the employee parks irregularly and 0.78 is the probability that the driver is not fined (1-0.22).
We want the probability that he is not fined 7 times so we are looking for P(X=7).
$\displaystyle P(X=x) = {{n}\choose {x}}\theta^{x}(1-\theta)^{n-x} $
$\displaystyle P(X=7) = {{7}\choose {7}}\ 0.78^7 = 0.78^{7} $
Alternatively just understand that if the employee parks 7 times with probability 0.78 of not getting fined you can work out the total probability by simply calculating $\displaystyle 0.78^{7}$.