Question

A certain bag of gemstones is composed of two-thirds diamonds and one-third rubies. If the probability of randomly selecting two diamonds from the bag, without replacement, is 5/12, what is the probability of selecting two rubies from the bag, without replacement?

Answer 1

Ans = 1/12

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