Subject: General Aptitude · Chapter: Probability · Exam: 2010 · Marks: · Difficulty:
An urn contains 6 red, 4 blue, 2 green and 3 yellow marbles. If two marbles are drawn at random from the urn, what is the probability that both are red?
(a)$\frac{1}{6}$
(b)$\frac{1}{7}$
(c)$\frac{2}{15}$
(d)$\frac{2}{5}$
(e)None of these
Answer
Answer (as printed): B
Explanation
Total number of balls $=(6+4+2+3)=15$. Let $E$ be the event of drawing 2 red balls. Then, $n(E)={ }^{6} C_{2}=\frac{6 \times 5}{2 \times 1}=15$. Also, $n(S)={ }^{15} C_{2}=\frac{15 \times 14}{2 \times 1}=105$. $$\therefore \quad P(E)=\frac{n(E)}{n(S)}=\frac{15}{105}=\frac{1}{7} .$$
Explanation as extracted from the printed page; notation may be imperfect.