Question

A bag contains $4$ white balls, $5$ red balls, $8$ black balls, and $3$ blue balls. A ball is drawn at random from the bag. Find the probability that the ball drawn is white, red or blue, not black, and neither black nor red

Answer 1

Step 1: Use formula for probability:

The formula for probability is,

$\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Step 2: Find the probability of the ball drawn is white:

Given that, the bag contains $4$ white balls, $5$ red balls, $8$ black balls, and $3$ blue balls..

Thus, the total number of outcomes will be $4+5+8+3=20$

Number of favorable events $=4$

Let, $A$ be the favorable event such that it is white.

$$\begin{gathered} P\left(A\right)=\frac{4}{20} \\ =\frac{1}{5} \end{gathered}$$

Step 3: Find the probability of the ball drawn is red or blue:

Number of favorable events $=5+3=8$

Let $B$ be the favorable event such that it is red or blue

$$\begin{gathered} P\left(B\right)=\frac{8}{20} \\ =\frac{2}{5} \end{gathered}$$

Step 4: Find the probability of the ball drawn is not black:

Not black is nothing but red or blue or white.

Let $C$ be the favorable event such that it is not black.

Number of favorable events $=n\left(C\right)=4+5+3=12$

$$\begin{gathered} P\left(C\right)=\frac{12}{20} \\ =\frac{6}{10} \\ =\frac{3}{5} \end{gathered}$$

Step 5: Find the probability of the ball drawn is neither black nor red:

Let $D$ be the favorable event such that it is not black.

Number of favorable events $=n\left(D\right)=4+3=7$

$P\left(D\right)=\frac{7}{20}$

Hence, from the above conclusions, the probability that the ball drawn is white is $\frac{1}{5}$, red or blue is $\frac{2}{5}$, not black is $\frac{3}{5}$, and neither black nor red is $\frac{7}{20}$.