Question

A bag contains $5$ red, $4$ blue and $3$ green balls. One ball is drawn at random. What is the probability of getting a blue ball?

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

Hint:

Probability always lies between $0$ and $1$. If your result is greater than $1$ or negative, you have likely made a calculation error!

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Probability is the measure of the likelihood that an event will occur.
It is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes.
Step 2: Key Formula or Approach:
The probability of an event \( P(E) \) is calculated as:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \] Step 3: Detailed Explanation:
First, we find the total number of possible outcomes, which is the total count of balls in the bag:
\[ \text{Total balls} = 5\ (\text{Red}) + 4\ (\text{Blue}) + 3\ (\text{Green}) = 12 \] The event of interest is drawing a blue ball.
The number of favorable outcomes (Blue balls) is 4.
Using the probability formula:
\[ P(\text{Blue}) = \frac{4}{12} \] To simplify the fraction, divide both the numerator and the denominator by their greatest common divisor, which is 4:
\[ P(\text{Blue}) = \frac{4 \div 4}{12 \div 4} = \frac{1}{3} \] While option (C) \( \frac{4}{12} \) is the unsimplified version, the correct simplified result matches option (B).
Step 4: Final Answer:
The probability of getting a blue ball is $\frac{1}{3}$.