Finding Probability . Is my answer correct?

Question

An automobile manufacturing plant produced 30 vehicles today: 9 were sedans, 11 were vans, and 10 were trucks. Plant managers are going to choose two of these vehicles for thorough inspection. The first vehicle will be chosen at random, and then the second vehicle will be chosen at random from the remaining vehicles. What is the probability that two trucks will be selected?

Report your answer as an exact fraction.

$P(T_1 \cap T_2)=\frac{10}{30}\cdot\frac 9 {29} = \frac 3 {29}$

Is my answer correct?

Answer 1

Yes it is correct.

It is more complete to write:$$P(T_1\cap T_2)=P(T_1)P(T_2\mid T_1)=\frac{10}{30}\frac{9}{29}$$

Answer 2

Your answer is correct. You have used multiplicative rule correctly.

$$P(T_1 \cap T_2) = P(T_1) P(T_2|T_1)$$