Sure, let's solve this step-by-step:
1. Identify the total number of balls in the box:
There are 15 white balls and 25 black balls. To determine the total number of balls, we add the number of white balls to the number of black balls:
[tex]\[
\text{Total number of balls} = 15 + 25 = 40
\][/tex]
2. Determine the favorable outcomes:
The favorable outcome is selecting a white ball. The number of white balls is given as 15.
3. Determine the total number of possible outcomes:
The total number of possible outcomes is the total number of balls in the box, which we've already calculated to be 40.
4. Calculate the probability:
Probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. Here, the favorable outcomes (selecting a white ball) are 15 and the total possible outcomes (total number of balls) are 40.
[tex]\[
\text{Probability of selecting a white ball} = \frac{\text{Number of white balls}}{\text{Total number of balls}} = \frac{15}{40}
\][/tex]
To simplify this fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 5:
[tex]\[
\frac{15}{40} = \frac{15 \div 5}{40 \div 5} = \frac{3}{8}
\][/tex]
As a decimal, this is:
[tex]\[
\frac{3}{8} = 0.375
\][/tex]
So, the probability of selecting a white ball from the box is [tex]\(0.375\)[/tex].
Therefore, the total number of balls is 40, and the probability of selecting a white ball is [tex]\(0.375\)[/tex].
