A bag contains 4 red, 5 blue and 3 green balls. If two balls are drawn at random from the bag, then which of the following statements are correct?

(A) The probability that both balls are red is 1/11.

(B) The probability that one ball is red, and one ball is blue is 10/33

(C) The probability that both balls are blue is 5/33.

(D) The probability that both balls are green is 5/11.

Choose the correct answer from the options given below:

Red balls = 4

Blue balls = 5

Green balls = 3

Total balls = 12

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When drawing 2 balls from 12 balls, the total number of ways is:

Total ways = $C(12,2)$

$= \dfrac{12 \times 11}{2 \times 1}$

$= \dfrac{132}{2}$

$= 66$

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Statement (A): Both balls are red = $\dfrac{1}{11}$

Ways to choose 2 red from 4 red balls:

$C(4,2)$

$= \dfrac{4 \times 3}{2 \times 1}$

$= 6$

Probability $= \dfrac{6}{66} = \dfrac{1}{11}$

Statement (A) is correct.

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Statement (B): One red and one blue = $\dfrac{10}{33}$

Ways to choose 1 red from 4 = 4

Ways to choose 1 blue from 5 = 5

Total ways = $4 \times 5 = 20$

Probability $= \dfrac{20}{66} = \dfrac{10}{33}$

Statement (B) is correct.

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Statement (C): Both balls are blue = $\dfrac{5}{33}$

Ways to choose 2 blue from 5 blue balls:

$C(5,2)$

$= \dfrac{5 \times 4}{2 \times 1}$

$= 10$

Probability $= \dfrac{10}{66} = \dfrac{5}{33}$

Statement (C) is correct.

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Statement (D): Both balls are green = $\dfrac{5}{11}$

Ways to choose 2 green from 3 green balls:

$C(3,2)$

$= \dfrac{3 \times 2}{2 \times 1}$

$= 3$

Probability $= \dfrac{3}{66} = \dfrac{1}{22}$

This is not equal to $\dfrac{5}{11}$.

Statement (D) is incorrect.

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Statements (A), (B) and (C) are correct.