In a bag, there are 5 red, 3 blue, and 2 green balls. What is ... | Mathematics MCQ | Examoogle

MathematicsProbability

In a bag, there are 5 red, 3 blue, and 2 green balls. What is the probability of picking a blue ball?

$\frac{3}{10}$

$\frac{1}{2}$

$\frac{1}{5}$

$\frac{3}{5}$

Correct Answer

⚙️ TE • Technical Direct FormulaMathematicsProbability

Option A

$\frac{3}{10}$

Quick Summary:

Directly sum all the given quantities for the denominator and place the target count in the numerator without complex working.

📐MAMath SolutionDirect Formula

📋 Given

Number of red balls = 5, blue balls = 3, and green balls = 2

🔢 Formula Used

P=n(E)n(S)P = \frac{n(E)}{n(S)}P=n(S)n(E)​

⚡ Exam Hall Shortcut / Speed Trick

Directly sum all the given quantities for the denominator and place the target count in the numerator without complex working.

⚠️ Common Student Trap / Pitfall

Confusing the total sample space by forgetting to add one of the color groups together.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate Total Outcomes

Add the number of red, blue, and green balls to find the total sample space size: $5 + 3 + 2 = 10$ .

n(S)=5+3+2=10n(S) = 5 + 3 + 2 = 10n(S)=5+3+2=10

Identify Favorable Outcomes

The number of blue balls given in the question is $3$ , which represents our favorable outcomes $n(E)$ .

n(E)=3n(E) = 3n(E)=3

Calculate Probability

Substitute the values into the probability formula: $P = \frac{3}{10}$ .

P=310P = \frac{3}{10}P=103​

✅

A is correct because the probability is calculated as the number of blue balls divided by the total number of balls, yielding $\frac{3}{10}$ .

Core Concepts Used

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💡 EXAM TIP

Basic probability questions frequently build into more complex conditional probability and combinatorial counting problems in competitive exams.

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