A bag contains 5 red balls, 8 white balls, 4 green balls and 7 black balls. If one ball is drawn at random, find the probability that it is not green

Options

A. `1/6`
B. `5/6`
C. `5/8`
D. `1/2`

Answer

To find the probability that a ball drawn from the bag is not green, we can follow these steps:

### Step 1: Determine the total number of balls in the bag.
- Count the number of each color of balls:
- Red balls = 5
- White balls = 8
- Green balls = 4
- Black balls = 7

**Total number of balls = Red + White + Green + Black**
\[ \text{Total} = 5 + 8 + 4 + 7 = 24 \]

### Step 2: Determine the number of balls that are not green.
- Since there are 4 green balls, we can find the number of balls that are not green by subtracting the number of green balls from the total number of balls.

**Number of not green balls = Total balls - Green balls**
\[ \text{Not green} = 24 - 4 = 20 \]

### Step 3: Calculate the probability of drawing a ball that is not green.
- Probability is calculated using the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
- In this case, the number of favorable outcomes is the number of not green balls, and the total number of outcomes is the total number of balls.

**Probability of not green = \(\frac{\text{Not green}}{\text{Total}}\)**
\[ \text{Probability} = \frac{20}{24} \]

### Step 4: Simplify the fraction.
- We can simplify \(\frac{20}{24}\) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4.

\[ \frac{20 \div 4}{24 \div 4} = \frac{5}{6} \]

### Final Answer:
The probability that the ball drawn is not green is \(\frac{5}{6}\).

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