Subject: General Aptitude · Chapter: Probability · Exam: · Marks: · Difficulty:
A bag contains 6 white and 4 black balls. Two balls are drawn at random. Find the probability that they are of the same colour.
Answer
Answer (as printed):
Explanation
Let $S$ be the sample space. Then, $n(s)=$ Number of ways of drawing 2 balls out of $(6+4)={ }^{10} C_{2}=\frac{(10 \times 9)}{(2 \times 1)}=45$. Let $E=$ Event of getting both balls of the same colour. Then, $n(E)=$ Number of ways of drawing (2 balls out of 6) or (2 balls out of 4) $=\left({ }^{6} C_{2}+{ }^{4} C_{2}\right)=\frac{(6 \times 5)}{(2 \times 1)}+\frac{(4 \times 3)}{(2 \times 1)}=(15+6)=21$. $\therefore P(E)=\frac{n(E)}{n(S)}=\frac{21}{45}=\frac{7}{15}$.
Explanation as extracted from the printed page; notation may be imperfect.