A box contains 5 red , 8 white and 4 green balls . A ball is drawn at random. Find the probability of getting a red ball. Also find the probability that the ball is not green .

Answer

To solve the problem, we need to find two probabilities:

1. The probability of drawing a red ball.
2. The probability of drawing a ball that is not green.

Let's break this down step by step.

### Step 1: Determine the total number of balls in the box.
- The box contains:
- 5 red balls
- 8 white balls
- 4 green balls

**Total number of balls = Number of red balls + Number of white balls + Number of green balls**

\[ \text{Total number of balls} = 5 + 8 + 4 = 17 \]

### Step 2: Calculate the probability of drawing a red ball.
- The probability of an event is given by the formula:

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

- Here, the number of favorable outcomes for drawing a red ball is 5 (since there are 5 red balls).

\[ P(\text{Red ball}) = \frac{5}{17} \]

### Step 3: Calculate the probability of drawing a ball that is not green.
- First, we find the probability of drawing a green ball.
- The number of favorable outcomes for drawing a green ball is 4.

\[ P(\text{Green ball}) = \frac{4}{17} \]

- To find the probability of not drawing a green ball, we can use the complement rule:

\[ P(\text{Not green}) = 1 - P(\text{Green}) \]

\[ P(\text{Not green}) = 1 - \frac{4}{17} = \frac{17 - 4}{17} = \frac{13}{17} \]

### Final Answers:
- Probability of drawing a red ball: \( \frac{5}{17} \)
- Probability of drawing a ball that is not green: \( \frac{13}{17} \)

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