Subject: General Aptitude · Chapter: Probability · Exam: 2010 · Marks: · Difficulty:
A basket contains 4 red, 5 blue and 3 green marbles. If 2 marbles are drawn atrandom from the basket, what is the probability that both are red?
(a)$\frac{3}{7}$
(b)$\frac{1}{2}$
(c)$\frac{1}{11}$
(d)$\frac{1}{6}$
(e)None of these
Answer
Answer (as printed): C
Explanation
Total number of balls $=(4+5+3)=12$. Let $E$ be the event of drawing 2 red balls. Then, $n(E)={ }^{4} C_{2}=\frac{4 \times 3}{2 \times 1}=6$. Also, $n(S)={ }^{12} C_{2}=\frac{12 \times 11}{2 \times 1}=66$. $$\therefore P(E)=\frac{n(E)}{n(S)}=\frac{6}{66}=\frac{1}{11} .$$
Explanation as extracted from the printed page; notation may be imperfect.