In your (imaginary) neighbourhood, the general consensus seems to be that 4 out of 5 cars are in good working order. The price for a good second-hand car is 2000$, while malfunctioning ones typically fetch 600$.

(a) What is the expected value of a used car

1280

That's wrong

To calculate the expected value of a used car, we need to consider the probabilities and the corresponding values associated with each outcome.

In this case, we know that 4 out of 5 cars are in good working order, meaning there is a probability of 4/5 (or 0.8) that a car will be in good condition. On the other hand, the probability of a car being in a malfunctioning condition is 1/5 (or 0.2), since there are 5 cars and 1 is malfunctioning according to the given information.

The value associated with a good second-hand car is $2000, while the value of a malfunctioning car is $600.

To calculate the expected value, we multiply each possible value by its corresponding probability and sum them up:

Expected value = (Probability of a good car * Value of a good car) + (Probability of a malfunctioning car * Value of a malfunctioning car)

Expected value = (0.8 * $2000) + (0.2 * $600)

Expected value = $1600 + $120

Expected value = $1720

Therefore, the expected value of a used car in this scenario is $1720.