calculating probability of profit

Question

lets say I rent out a car. The car cost me 100\$ to buy and no other costs are involved. When I rent out the car I make 50\$ a month. The car might break down and I cannot fix it after that so what profit I make when the car breaks is the total profit on that car.

As an example, from previous experience I know that the probability of this car breaking before discrete points in time. 1 month = 20%, 2 months = 40%, 3 months = 50%, 4 months = 60%, etc.

How would I do the calculation on my expected profit from this? As an added question, I have only ever owned a car for less than 7 months, after that I might have sold it so I do not know the probability after this. Can i still find some total expected profit somehow?

Answer 1

One approach would be to find the probability the car stops earning after a given number of months, perhaps (if I have read your description of the probabilities correctly)

months cum.prob prob
  1      0.2     0.2
  2      0.4     0.2
  3      0.5     0.1
  4      0.6     0.1
  5      0.7     0.1
  6      0.8     0.1
  7      1.0     0.2

so the expected number of months earning: $$1 \times 0.2+2 \times 0.2 +3 \times 0.1 +4 \times 0.1 +5 \times 0.1 +6 \times 0.1 +7 \times 0.2 =3.8$$

and thus an expected net profit of $$\$50 \times 3.8 - \$100= \$90$$