A bag has 45 discs.
Let the number of y ( yellow discs ) be x.
Then the probability of choosing a y is P(y) = x/45
And the probability of choosing a b is P(b) = (45-x)/45 = 1- p(y).
If two were choosing randomly without replacement.
Then the probability if choosing the 2nd yellow = (x-1)/44
Given that the probability of getting 2 y =1/15.
But we know that the probability of choosing 2 yellow = probability of choosing the first yellow * probability of choosing the 2nd yellow.
P(2 y) = P (1st y) * P( 2nd y)
= x/45 * (x-1)/ 44 = 1/15
==> x(x-1) / 45*44 = 1/15
Let us cross multiply.
==> x(x-1) = 45*44/15 = 132
==> x^2 -x -132 = 0
Now we will factor the quadratic equation.
==> (x-12)(x+11) = 0
==> x1= 12
==> x2 = -11 ( Not valid because the number of discs can not be negative.
Then, there are 12 yellow discs in the bag.