Final answer:
The probability of selecting a truck and then a compact from Jalen's used car lot is calculated by multiplying the probability of each event. The total probability is the product of the probability of drawing a truck first (29/83) and then a compact (31/82).
Step-by-step explanation:
The question asks about the probability of selecting a truck first and then a compact from the car lot. To find this probability, we need to consider the total number of vehicles and the selection process, which is without replacement since the first vehicle is not put back into the lot before selecting the second one.
The total number of vehicles on the lot is the sum of all types of vehicles: 31 compacts + 23 sedans + 29 trucks = 83 vehicles. The probability of selecting a truck first is the number of trucks over the total number of vehicles, which is 29/83. Once a truck is selected, there are now 82 vehicles remaining. The probability of then selecting a compact is the number of compacts over the remaining number of vehicles, which is 31/82. To find the combined probability of both events happening, we multiply the probabilities together:
Probability(truck then compact) = (29/83) * (31/82)
This gives us the probability of selecting a truck first and then a compact as a reduced fraction. Note that the fractions should be reduced to simplest form if they can be simplified further.