Problem:
A bag contains 8 red balls and some white balls. The probability of drawing a white ball is half that of drawing a red ball. Determine the number of white balls in the bag.

Solution:

Step 1: Set up the problem
Let's assume the number of white balls in the bag is 'w'. Given that the probability of drawing a white ball is half that of drawing a red ball, we can write the following equation:

P(white ball) = 1/2 * P(red ball)

Step 2: Calculate the probabilities
The probability of drawing a white ball can be calculated as the number of white balls divided by the total number of balls:

P(white ball) = w / (8 + w)

Similarly, the probability of drawing a red ball can be calculated as the number of red balls divided by the total number of balls:

P(red ball) = 8 / (8 + w)

Step 3: Substitute the probabilities into the equation
Substituting the calculated probabilities into the equation from Step 1, we get:

w / (8 + w) = 1/2 * (8 / (8 + w))

Step 4: Solve the equation
To solve the equation, we can cross-multiply:

2w = 8

Dividing both sides by 2, we get:

w = 4

Step 5: Answer
Therefore, there are 4 white balls in the bag.

Explanation:
- The problem presents a bag containing 8 red balls and an unknown number of white balls.
- The probability of drawing a white ball is given as half that of drawing a red ball.
- To determine the number of white balls, we set up an equation using probabilities.
- By substituting the probabilities and simplifying the equation, we find that the number of white balls is 4.
- The solution is obtained by solving the equation algebraically.
- The explanation outlines the steps taken to solve the problem and provides a clear answer.

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