The all Washed-Up Car Wash has found a tremendous bargain on a new car waxing machine imported from the newly independent Republic of Lowenbrau. The only weak point is the special wax pump, which can be expected to fail relatively frequently and cannot be repaired. AWUCW can order up to five replacement pumps at a time, which would be delivered with the annual end of year shipment from Lowenbrau. They are available at no other time, and are expensive. If the wax pump fails and they have no replacement, they must stop using the machine until the next shipment arrives. The probabilities of breakdowns during any given year are given below:
|
Breakdowns per year
|
Probability
|
|
0
|
0.30
|
|
1
|
0.25
|
|
2
|
0.15
|
|
3
|
0.12
|
|
4
|
0.10
|
|
5
|
0.08
|
|
Sum
|
1.00
|
In an average year, how many pumps can they expect to fail?