Question

Problem PageQuestion An automobile manufacturing plant produced 34 vehicles today: 16 were motorcycles, 9 were trucks, and 9 were vans. 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 motorcycle and the second vehicle is a van?

Answer 1

Answer:

Probability that the first vehicle selected is a motorcycle and the second vehicle is a van is (24/187) or 0.1283.

Step-by-step explanation:

We are given that an automobile manufacturing plant produced 34 vehicles today: 16 were motorcycles, 9 were trucks, and 9 were vans.

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.

As we know that, Probability of any event  =  $\frac{\text{Favorable number of outcomes}}{\text{Total number of outcomes}}$

Now, Probability that the first vehicle selected is a motorcycle is given by;

                   =  $\frac{\text{Number of motorcycles}}{\text{Total number of vehicles}}$

Here, Number of motorcycles = 16

Total number of vehicles = 16 + 9 + 9 = 34

So, Probability that the first vehicle selected is a motorcycle =  $\frac{16}{34}$

Similarly, Probability that the second vehicle is a van is given by;

              =   $\frac{\text{Number of vans}}{\text{Total number of remaining vehicles}}$

Here, Number of vans = 9

And Total number of remaining vehicles after selecting one motorcycle = 34 - 1 = 33

So, Probability that the second vehicle selected is a van =  $\frac{9}{33}$

Therefore, the probability that the first vehicle selected is a motorcycle and the second vehicle is a van  =  $\frac{16}{34}\times \frac{9}{33}$

                                               =  $\frac{24}{187}$  =  0.1283