Question

an automobile manufacturing plant produced 33 vehicles today: 10 were trucks, 6 were motorcycles, and 17 were vans. (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 two motorcycles will be selected?

do not round your intermediate computations. round your final answer to three decimal places.

(if necessary, consult a list of formulas.)

Explanation:

Identify the given values

Using the Probability of Events knowledge point

$$
LATEXBLOCK0
$$

Calculate the first probability

Using the Probability of Events knowledge point

$$ P(M_1) = \frac{6}{33} $$

Calculate the second probability

Using the Dependent Events knowledge point

$$ P(M_2 \mid M_1) = \frac{5}{32} $$

Compute the joint probability

Using the Dependent Events knowledge point

$$
LATEXBLOCK1
$$

Round the final answer

Using the Probability of Events knowledge point

$$ P(\text{two motorcycles}) \approx 0.028 $$

Answer:

An automobile manufacturing plant produced 33 vehicles today: 10 were trucks, 6 were motorcycles, and 17 were vans. (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 two motorcycles will be selected?

Do not round your intermediate computations. Round your final answer to three decimal places.

(If necessary, consult a list of formulas.)

<blank>0.028</blank>