A bag contains 5 red balls, 4 green balls, and 3 blue balls. If two balls are drawn at random without replacement, the probability that both balls are red is:
Options:
(A) $\frac{5}{33}$
(B) $\frac{5}{36}$
(C) $\frac{1}{6}$
(D) $\frac{10}{33}$
Answer Key:
A
Step-by-Step Solution & Explanation
Total number of balls $= 5 + 4 + 3 = 12$.
Probability of drawing two red balls:
$P(\text{both red}) = \frac{\binom{5}{2}}{\binom{12}{2}} = \frac{\frac{5 \times 4}{2}}{\frac{12 \times 11}{2}} = \frac{10}{66} = \frac{5}{33}$