Answer:
Ans = 1/12
Step-by-step explanation:
Diamonds = 2/3 of gemstones
Ruby = 1/3 of gemstones
Diamond = 2x
Rubyb= x
Probability of picking two diamonds = 5/12
(2x / 3x )* (2x-1)/ (3x -1) = 5/12
(4x^2 -2x) / (9x^2 -3x ) = 5/12
12(4x^2 - 2x ) = 5(9x^2 - 3x)
48x^2 - 24x = 45x^2 - 15x
48x^2 - 45x^2 - 24x + 15x = 0
3x^2 - 9x = 0
3x(x - 3) = 0
3x = 0 or (x - 3) = 0
x = 0 or x = 3
Diamond = 2x = 2(3) = 6
Ruby = x = 3
Total number of gemstones = 6+3 = 9
probability of getting 2 rubies =3/9 * 2/8
= 6/72
= 1/12
