An urn contains 2 red , 3 green and 2 blue balls . If a ball is drawn at random , then find the probability that the ball is not blue .

Options

A. `5/7`
B. `10/21`
C. `2/7`
D. `11/21`

Answer

To find the probability that a ball drawn at random from the urn is not blue, we can follow these steps:

### Step 1: Determine the total number of balls in the urn.
- The urn contains:
- 2 red balls
- 3 green balls
- 2 blue balls

**Total number of balls = Number of red balls + Number of green balls + Number of blue balls**
\[ \text{Total} = 2 + 3 + 2 = 7 \]

### Step 2: Determine the number of favorable outcomes.
- We need to find the number of balls that are not blue.
- The non-blue balls consist of:
- 2 red balls
- 3 green balls

**Total number of non-blue balls = Number of red balls + Number of green balls**
\[ \text{Non-blue balls} = 2 + 3 = 5 \]

### Step 3: Calculate the probability.
- The probability of an event is given by 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 non-blue balls, and the total number of outcomes is the total number of balls.

\[ \text{Probability (not blue)} = \frac{\text{Non-blue balls}}{\text{Total balls}} = \frac{5}{7} \]

### Final Answer:
The probability that the ball drawn is not blue is \(\frac{5}{7}\).

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