Question

there are 36 disks in a bag. some of them are black and the rest are white. two are simultaneously selected at random. given that the probability of selecting two disks of the same colour is equal to the probability of selecting two disks of different colour, how many black disks are there in the bag?

Answer 1

There are 16 black disks in the bag.

Step-by-step explanation:

Let's assume that there are x black disks in the bag.

The total number of disks in the bag is 36, so the number of white disks is 36 - x.

The probability of selecting two disks of the same color is given by the equation:
(x/36) * ((x-1)/(36-1)) = ((36-x)/36) * ((36-x-1)/(36-1))

Simplifying the equation, we get:
x(x-1) = (36-x)(36-x-1)

Expanding and rearranging the equation, we get:
x^2 - 37x + 648 = 0

Solving this quadratic equation, we find that x = 16.

Therefore, there are 16 black disks in the bag.