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 a 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: Determining Total and Favorable Outcomes:
First, find the total number of balls in the bag: \[ \text{Total balls} = 5\ (\text{red}) + 4\ (\text{blue}) + 3\ (\text{green}) = 12 \] Next, identify the number of favorable outcomes (blue balls): \[ \text{Number of blue balls} = 4 \]

Step 3: Calculating Probability:
The formula for probability ($P$) is: \[ P(\text{Blue}) = \frac{\text{Number of Blue Balls}}{\text{Total Number of Balls}} \] \[ P(\text{Blue}) = \frac{4}{12} \] Simplifying the fraction by dividing both the numerator and denominator by $4$: \[ P(\text{Blue}) = \frac{1}{3} \]

Step 4: Final Answer:
The probability of getting a blue ball is $\frac{1}{3}$ (which is also equal to $\frac{4}{12}$). Both options (B) and (C) represent this value, but (B) is the simplified form.