Question

A bag contains $5$ white balls, $7$ red balls, $4$ black balls, and $2$ blue balls. One ball is drawn at random from the bag. What is the probability that the ball drawn is white or blue, red or black, not white, neither white nor black.

Answer 1

Step 1: Use the formula for probability and find the total number of outcomes:

The formula for probability is,

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

Given that, the bag contains $5$ white balls, $7$ red balls, $4$ black balls, and $2$ blue balls.

The total number of balls$=5+7+4+2=18$

Thus, the total number of outcomes will be $18.$

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

Number of balls that are white or blue $=5+2=7$
Thus the required probability$=\frac{7}{18}$
Step 3: Find the probability of the ball drawn is red or black:

Number of balls that are red or black $=7+4=11$
Thus, the required probability$=\frac{11}{18}$

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

Number of balls that are not white$=7+4+2=13$
Thus, the required probability $=\frac{13}{18}$

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

Number of balls that are neither white nor black$=7+2=9$
Therefore, the required probability

$$\begin{gathered} =\frac{9}{18} \\ =\frac{1}{2} \end{gathered}$$

Hence, from the above conclusions, the probability that the ball drawn is white or blue is $\frac{7}{18}$, red or black is $\frac{11}{18}$, not white is $\frac{13}{18}$, and neither white nor black is $\frac{1}{2}$