Question

A bag contains 5 black balls, 4 white balls and 3 red balls, If a ball is selected randomwise, the probability that it is black or red ball is

• A. $\frac{1}{3}$
• B. $\frac{1}{4}$
• C. $\frac{5}{12}$
• D. $\frac{2}{3}$

Answer 1

The correct option is D

$\frac{2}{3}$

Out of 12 balls, one ball can be drawn in ${}^{12}{C}_1$ ways.

$\therefore$ Total number of elementary events

${=}^{12}{C}_1=12$

Out of five black balls, one black ball can be chosen in ${}^5{C}_1=5$ ways.

Out of three red balls, one red ball can be chosen in ${}^3{C}_1=3$ ways.

$\therefore$ Favourable number of events = 5 + 3 = 8

Hence, required probability $=\frac{8}{12}=\frac{2}{3}$