A bag contains 4 red, 5 blue and 3 green balls. If two balls are draw…

The correct answer is Option (1) → (A), (B) and (C) only

Two balls drawn together form a selection, so combinations are counted. The bag has \(4+5+3=12\) balls, and the probability of each event is the number of favourable pairs divided by the number of all pairs.

• All pairs: \(\displaystyle {}^{12}C_{2}=\frac{12\times11}{2}=66\)

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

• Red pairs \(={}^{4}C_{2}=6\)

• Probability \(=\frac{6}{66}=\frac{1}{11}\)

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

• Any of the 4 red balls can go with any of the 5 blue ones: \(4\times5=20\) pairs

• Probability \(=\frac{20}{66}=\frac{10}{33}\)

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

• Blue pairs \(={}^{5}C_{2}=10\)

• Probability \(=\frac{10}{66}=\frac{5}{33}\)

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

• There are only 3 green balls, so green pairs \(={}^{3}C_{2}=3\)

• The probability is \(\frac{3}{66}=\frac{1}{22}\), not 5/11