Question

A used car lot has 12 red cars, 9 silver cars, and 4 black cars. If two cars are selected at random to be displayed in the showroom, what is the probability they are the same color?

Answer 1

All in all, if we sum up the cars in the car lot, there are 25. Selecting two cars at random, will give us the sample space is, 
                             25C2 = 300
Hence, there are 300 ways in which the cars ban be selected. 
  (RED)                              (12C2) / 300 = 11/50
   (SILVER)                         (9C2) / 300 = 3/25
   (BLACK)                          (4C2) / 300 = 1/50

Adding up all the values will give us answer of 0.36. 

Answer 2

Answer:  0.36

Step-by-step explanation:

Given : Number of red cars = 12

Number of silver cars = 9

Number of black cars = 4

Total number of cars : $12+9+4=25$

Number of ways of selecting two cars :-

$^{25}C_2=\dfrac{25!}{2!(25-2)!}=300$

Number of ways of selecting two cars of same color :-

$^{12}C_2+^{9}C_2+^4C_2\\\\=\dfrac{12!}{2!(12-2)!}+\dfrac{9!}{2!(9-2)!}+\dfrac{4!}{2!(4-2)!}\\\\=66+36+6=108$

Now, the probability two cars are selected at random to be displayed in the showroom are the same color:-

$\dfrac{108}{300}=0.36$