Question

A bag contains 4 red, 5 blue and 3 green balls. One ball is drawn at random. The probability of getting a blue ball is:

• A. $\frac{1}{4}$
• B. $\frac{1}{3}$
• C. $\frac{5}{12}$
• D. $\frac{1}{2}$

Hint:

Always calculate the total sample pool size first. Once you know the denominator is 12, check if your target item count (5) can be simplified with it. Since 5 is a prime number, the fraction must remain exactly as $\frac{5}{12}$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Probability calculates the likelihood of picking a target outcome from an entire set of mixed items. It is defined mathematically as the ratio of the number of favorable elements (the specific items you want to pick) to the total number of all available elements present in the sample pool.

Step 2: Key Formula or Approach:
$$\text{Probability (P)} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$

Step 3: Detailed Explanation:
First, count all the separate colored items in the bag to find the total sample space size: $\text{Red balls} = 4$ $\text{Blue balls} = 5$ $\text{Green balls} = 3$ \[ \text{Total number of balls} = 4 + 5 + 3 = 12 \] Next, identify the number of favorable outcomes. Since we are calculating the probability of drawing a blue ball, the count of blue balls represents our favorable outcomes: \[ \text{Number of favorable outcomes} = 5 \] Apply these values to the probability formula: \[ P(\text{Blue}) = \frac{5}{12} \] This fraction cannot be simplified further, matching option (c).

Step 4: Final Answer:
The probability of getting a blue ball is $\frac{5}{12}$.