A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?

Options

A. `3/4`
B. `4/7`
C. `1/8`
D. `3/7`

Answer

To solve the problem step by step, we will calculate the probability of drawing a white ball from the bag.

### Step 1: Identify the number of balls
- The bag contains 6 black balls and 8 white balls.

### Step 2: Calculate the total number of balls
- Total number of balls = Number of black balls + Number of white balls
- Total number of balls = 6 + 8 = 14

### Step 3: Identify the number of favorable outcomes
- The favorable outcomes for drawing a white ball is the number of white balls.
- Number of favorable outcomes = Number of white balls = 8

### Step 4: Calculate the probability
- Probability (P) of drawing a white ball is given by the formula:

\[ P(\text{white ball}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

- Substituting the values we have:

\[ P(\text{white ball}) = \frac{8}{14} \]

### Step 5: Simplify the fraction
- To simplify \(\frac{8}{14}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2.

\[ P(\text{white ball}) = \frac{8 \div 2}{14 \div 2} = \frac{4}{7} \]

### Final Answer
- The probability that the ball drawn is white is \(\frac{4}{7}\).

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