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 white, red, not black, and red or white.

Answer 1

Step 1: Find the total number of possible outcomes:

We know that the formula for probability is,

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

Here, the bag contains $6$ red, $5$ black, and $4$ white balls.

Therefore, the total number of balls is,

$6+5+4=15$

Thus, the total number of possible outcomes is $15$

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

The number of favorable outcomes of getting a white ball is $4$

The probability that the ball drawn is white will be,

$=\frac{4}{15}$

Thus, the probability that the ball drawn is white is $\frac{4}{15}$

Step 3: Find the probability that the ball drawn is red:

The number of favorable outcomes of getting a red ball is $6$

The probability that the ball drawn is red will be

$$\begin{gathered} =\frac{6}{15} \\ =\frac{2}{5} \end{gathered}$$

Thus, the probability that the ball drawn is red is $\frac{2}{5}$

Step 4: Find the probability that the ball drawn is not a black one:

The number of favorable outcomes of getting a not a black ball is $4+6=10$

The probability that the ball drawn is not black will be,

$$\begin{gathered} =\frac{10}{15} \\ =\frac{2}{3} \end{gathered}$$

Thus, the probability that the ball drawn is not black is $\frac{2}{3}$

Step 5: Find the probability that the ball drawn is red or white::

The number of favorable outcomes of getting a white ball is $4$

The number of favorable outcomes of getting a red ball is $6$

The probability that the ball drawn is red or white is

$$\begin{gathered} =\frac{4}{15}+\frac{6}{15} \\ =\frac{4+6}{15} \\ =\frac{10}{15} \\ =\frac{2}{3} \end{gathered}$$

Thus, the probability that the ball drawn is red or white is $\frac{2}{3}$

Hence, from the above conclusions, the probability that the ball drawn is white is $\frac{4}{15}$, red is $\frac{2}{5}$, not a black one is $\frac{2}{3}$, and red or white is $\frac{2}{3}$