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

Answer: 0.36

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=(25!)/(2!(25-2)!)=300`

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

`^(12)C_2+^(9)C_2+^4C_2\\\\=(12!)/(2!(12-2)!)+(9!)/(2!(9-2)!)+(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:-

`(108)/(300)=0.36`

Answer 2

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.