Step 1: Understanding the Concept:
Probability is the measure of the likelihood that an event will occur. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes in the sample space.
Step 2: Key Formula or Approach:
\[ P(E) = \frac{n(E)}{n(S)} \]
Where \( n(E) \) is the number of favorable outcomes (blue balls) and \( n(S) \) is the total number of outcomes (total balls).
Step 3: Detailed Explanation:
1. Calculate Total Number of Outcomes (\( n(S) \)):
Total balls in the bag = Red balls + Blue balls + Green balls
Total = \( 5 + 4 + 3 = 12 \).
This means there are 12 equally likely outcomes when one ball is picked.
2. Identify Favorable Outcomes (\( n(E) \)):
The question asks for the probability of picking a blue ball.
Number of blue balls = 4.
So, \( n(E) = 4 \).
3. Calculate the Probability:
\[ P(\text{Blue}) = \frac{4}{12} \]
4. Simplification:
We simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4.
\[ \frac{4 \div 4}{12 \div 4} = \frac{1}{3} \]
Looking at the options, although (C) 4/12 is technically correct, (B) 1/3 is the simplified standard representation and is the intended answer for such exams.
Step 4: Final Answer:
The probability is 1/3.