Question

an automobile manufacturing plant produced 34 vehicles today: 16 were trucks, 9 were vans, and 9 were motorcycles. (each vehicle falls into only one of these categories.) plant managers are going to select two of these vehicles for a thorough inspection. the first vehicle will be selected at random, and then the second vehicle will be selected at random from the remaining vehicles. what is the probability that the first vehicle selected is a truck and the second vehicle is a motorcycle? do not round your intermediate computations. round your final answer to three decimal places.

Explanation:

Step1: Probability of first truck

There are 16 trucks out of 34 total vehicles. So the probability of selecting a truck first is $\frac{16}{34}$.

Step2: Probability of second motorcycle

After selecting a truck, there are 33 vehicles left, and 9 motorcycles. So the probability of selecting a motorcycle second is $\frac{9}{33}$.

Step3: Multiply the probabilities

To find the probability of both events happening, multiply the two probabilities: $\frac{16}{34} \times \frac{9}{33}$.
First, calculate $\frac{16}{34} \times \frac{9}{33} = \frac{16\times9}{34\times33} = \frac{144}{1122}$.
Simplify $\frac{144}{1122} \approx 0.12834$.

Answer:

0.128