A bag contains 3 red, balls, 4 bule balls and 5 green balls .What is the probability that a ball picked up at random is not a blue ball ?

Options

A. `(1)/(4)`
B. `(1)/(3)`
C. `(2)/(3)`
D. `(3)/(4)`

Answer

To solve the problem, we need to find the probability that a ball picked at random from the bag is not a blue ball. Let's break this down step by step.

### Step 1: Determine the total number of balls in the bag.
- The bag contains:
- 3 red balls
- 4 blue balls
- 5 green balls

**Total number of balls = 3 (red) + 4 (blue) + 5 (green) = 12 balls.**

### Step 2: Identify the number of favorable outcomes (not a blue ball).
- The favorable outcomes for picking a ball that is not blue include:
- All red balls (3)
- All green balls (5)

**Total number of favorable outcomes = 3 (red) + 5 (green) = 8 balls.**

### Step 3: Calculate the probability.
- Probability is calculated using the formula:
\[ P(\text{not a blue ball}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

- Substituting the values we found:
\[ P(\text{not a blue ball}) = \frac{8}{12} \]

### Step 4: Simplify the fraction.
- We can simplify \(\frac{8}{12}\) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4:
\[ P(\text{not a blue ball}) = \frac{8 \div 4}{12 \div 4} = \frac{2}{3} \]

### Final Answer:
The probability that a ball picked at random is not a blue ball is \(\frac{2}{3}\).

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