Question

An automobile manufacturing plant produced 30 vehicles today: 10 were sedans, 9 were vans, and 11 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?

Answer 1

Answer: $\dfrac{11}{87}$

Step-by-step explanation:

Given : An automobile manufacturing plant produced 30 vehicles today: 10 were sedans, 9 were vans, and 11 were trucks.

Number of combinations of n things taking r at a time :

$^nC_r=\dfrac{n!}{r!(n-r)!}$

Number of ways to choose two vehicles out of 30 vehicles :-

$^{30}C_2=\dfrac{30!}{2!(28)!}\\\\=\dfrac{30\times29}{2}\\\\=435$

Number of ways to choose two trucks out of 11 vehicles :-

$^{11}C_2=\dfrac{11!}{2!(9)!}\\\\=\dfrac{11\times10}{2}\\\\=55$

Now, the the probability that two trucks will be selected will be :-

$\dfrac{55}{435}=\dfrac{11}{87}$