MHB A bag contains x beads. Calculate the value of x.

[Help seeker]

A bag contains x beads. 6 of the beads are red and the rest are blue. Ravish is going to take at random 2 beads from the bag. The probability that the 2 beads will be of the same colour is $9 /17$
Using algebra calculate the value of x. ( show sworking if possible)

 

[HOI]

There are 6 red beads and x- 6 blue beads. The probability the first bead taken is red is 6/x. In that case there are 5 red beads and x- 6 blue beads left for a total of x-1 beads. The probability the second bead is also red is 5/(x- 1). The probability the two beads are both red is (6/x)(5/(x- 1))= 30/(x(x- 1)).

There are 6 red beads and x- 6 blue beads. The probability the first bead taken is blue is (x- 6)/x. In that case there are 6 red beads and x- 7 blue beads left for a total of x- 1 beads. The probability the second bead is also blue is (x- 7)/(x- 1). The probability the to beads are both blue is ((x- 6)/x)((x- 7)/(x- 1))= (x- 6)(x-7)/(x(x- 1).

The probability the two beads are the same color is 30/(x(x-1)+ ((x- 6)(x- 7)/(x(x-1))= (x^2- 13x+ 72)/(x^2- x).

Set that equal to 9/17 and solve for x.