A bag contains 3 white, 2 blue and 5 red balls. One ball is drawn at random from the bag. What is the probability that the ball drawn is not red?

Question

Accepted Answer

To determine the probability that the ball drawn from the bag is not red, we first need to understand the composition of the balls in the bag and the total number of balls.

The bag contains:
- 3 white balls
- 2 blue balls
- 5 red balls

The total number of balls in the bag is:
$$ 3 + 2 + 5 = 10 $$

The number of balls that are not red (i.e., white or blue) is:
$$ 3 \text{ (white)} + 2 \text{ (blue)} = 5 $$

The probability of drawing a ball that is not red is the ratio of the number of non-red balls to the total number of balls:
$$ \text{Probability (not red)} = \frac{\text{Number of non-red balls}}{\text{Total number of balls}} = \frac{5}{10} = \frac{1}{2} $$

Therefore, the correct answer is Option 4: $\frac{1}{2}$.

**Explanation for why each option is incorrect:**

1. **Option 1: $\frac{4}{5}$**
   - This option suggests that the probability of drawing a non-red ball is $\frac{4}{5}$. However, this would imply that there are 8 non-red balls out of 10, which is incorrect because there are only 5 non-red balls.

2. **Option 2: $\frac{3}{10}$**
   - This option suggests that the probability of drawing a non-red ball is $\frac{3}{10}$. This would mean there are 3 non-red balls out of 10, which is incorrect as there are actually 5 non-red balls.

3. **Option 3: $\frac{1}{5}$**
   - This option suggests that the probability of drawing a non-red ball is $\frac{1}{5}$. This would imply there is only 1 non-red ball out of 10, which is incorrect because there are 5 non-red balls.

By following the instructions and focusing on the given correct answer, we conclude that Option 4: $\frac{1}{2}$ is indeed the correct answer, as it accurately represents the probability of drawing a non-red ball from the bag.