Subject: General Aptitude · Chapter: Probability · Exam: · Marks: · Difficulty:
A box contains 10 black and 10 white balls. What is the probability of drawing 2 balls of the same colour?
(a)$\frac{9}{19}$
(b)$\frac{9}{38}$
(c)$\frac{10}{19}$
(d)$\frac{5}{19}$
(e)None of these
Answer
Answer (as printed): A
Explanation
Total number of balls $=(10+10)=20$. Let $E$ be the event of drawing 2 balls of the same colour. $n(E)=$ number of ways of drawing 2 black balls or 2 white balls $$n(E)=\left({ }^{10} C_{2}+{ }^{10} C_{2}\right)=2 \times{ }^{10} C_{2}=2 \times \frac{10 \times 9}{2 \times 1}=90 .$$ $n(S)=$ number of ways of drawing 2 balls out of 20 $$={ }^{20} C_{2}=\frac{20 \times 19}{2 \times 1}=190 . \therefore \quad P(E)=\frac{n(E)}{n(S)}=\frac{90}{190}=\frac{9}{19} .$$
Explanation as extracted from the printed page; notation may be imperfect.