A bag contains 24 balls of which x are red, 2x are white and 3x are blue balls. A ball is selected at random, the probability that it is not red, is :

Question

Accepted Answer

To determine the probability that a randomly selected ball from the bag is not red, we first need to understand the composition of the balls in the bag.

The bag contains:
- $ x $ red balls
- $ 2x $ white balls
- $ 3x $ blue balls

The total number of balls in the bag is given as 24. Therefore, we can set up the equation for the total number of balls:

$$ x + 2x + 3x = 24 $$

Simplifying this equation, we get:

$$ 6x = 24 $$

Solving for $ x $, we find:

$$ x = 4 $$

Now, substituting $ x = 4 $ back into the expressions for each color, we have:
- Red balls = $ x = 4 $
- White balls = $ 2x = 8 $
- Blue balls = $ 3x = 12 $

The probability that a randomly selected ball is not red is the probability that it is either white or blue. The number of non-red balls is the sum of the white and blue balls:

$$ 8 \text{ (white)} + 12 \text{ (blue)} = 20 \text{ (non-red balls)} $$

The probability of selecting a non-red ball is the ratio of non-red balls to the total number of balls:

$$ \text{Probability (not red)} = \frac{\text{Number of non-red balls}}{\text{Total number of balls}} = \frac{20}{24} $$

Simplifying this fraction, we divide both the numerator and the denominator by 4:

$$ \frac{20}{24} = \frac{5}{6} $$

Thus, the probability that a randomly selected ball is not red is $\frac{5}{6}$, which corresponds to Option 2.

**Explanation for Incorrect Options:**

1. **Option 1: $\frac{1}{6}$** - This option suggests a much lower probability than calculated. It would imply that only 4 out of 24 balls are non-red, which is incorrect as we have 20 non-red balls.

3. **Option 3: $\frac{1}{3}$** - This option suggests that only 8 out of 24 balls are non-red, which is incorrect. We have already established that there are 20 non-red balls.

4. **Option 4: $\frac{2}{3}$** - This option suggests that 16 out of 24 balls are non-red, which is incorrect. The correct number of non-red balls is 20.

Therefore, Option 2 is the correct answer, as it accurately represents the probability of selecting a non-red ball from the bag.