Question

A bag contains 4 red, 5 black and 6 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is: 

not black

Answer 1

\[\text{ Number of red balls }= 4\]
\[\text{ Number of black balls } = 5\]
\[\text{ Number of white balls } = 6\]
\[\text{ Total number of balls in the bag } = 4 + 5 + 6 = 15\]
\[\text{ Therefore, the total number of cases is 15 }. \]

\[\text{ Let C denote the event of getting a black ball }. \]
\[\text{ Number of  favourable outcomes .e number of black balls }=5\]
\[P\left( C \right) = \frac{\text{ Number of favourable outcomes }}{\text{ Total number of outcomes }} = \frac{5}{15} = \frac{1}{3}\]
\[\text{ Therefore, the probabilty of not getting a black ball is as follows }: \]
\[P\left( \bar{C} \right) = 1 - P\left( C \right) = 1 - \frac{1}{3} = \frac{2}{3}\]