Question

A bag contains $6$ red, $5$ black and $4$ white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is not black.

Answer 1

Step 1: Finding the total number of outcomes and the number of favourable outcomes

There are $6$ red, $5$ black and $4$ white balls in a bag.

$$\begin{gathered} TotalOutcomes=Redballs+Blackballs+Whiteballs \\ TotalOutcomes=6+5+4 \\ TotalOutcomes=15 \end{gathered}$$

So, the total number of outcomes is $15$.

The number of the drawn ball is not a black ball is $6+4=10$.

So, the number of favorable outcomes is $10$.

Step 2: Finding the probability of not getting a black ball

The formula for probability is,

$$\begin{gathered} \Rightarrow Probability=\frac{Numberoffavorableoutcomes}{Totalnumberofoutcomes} \\ \Rightarrow P(notblack)=\frac{10}{15} \\ \therefore P(notblack)=\frac{2}{3} \end{gathered}$$

Hence, the probability of not getting a black ball is $\frac{2}{3}.$