A bag contains 20 marbles numbered 1 to 20. If one marble is d... | Mathematics MCQ | Examoogle

MathematicsProbability

A bag contains 20 marbles numbered 1 to 20. If one marble is drawn, what is the probability that the number is a prime number?

$\frac{7}{20}$

$\frac{8}{20}$

$\frac{9}{20}$

$\frac{10}{20}$

Correct Answer

⚙️ TE • Technical Direct FormulaMathematicsProbability

Option B

$\frac{8}{20}$

Quick Summary:

Memorize prime numbers up to 20: 2, 3, 5, 7, 11, 13, 17, 19. Count them quickly as 8 and divide by total 20.

📐MAMath SolutionDirect Formula

📋 Given

A bag contains 20 marbles numbered 1 to 20.

🔢 Formula Used

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

⚡ Exam Hall Shortcut / Speed Trick

Memorize prime numbers up to 20: 2, 3, 5, 7, 11, 13, 17, 19. Count them quickly as 8 and divide by total 20.

⚠️ Common Student Trap / Pitfall

Many students include the number 1 as a prime number, which is incorrect as 1 is neither prime nor composite.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify Sample Space

Total number of outcomes in the set {1, 2, 3,..., 20} is $n(S) = 20$ .

n(S)=20n(S) = 20n(S)=20

List Prime Numbers

The prime numbers between 1 and 20 are 2, 3, 5, 7, 11, 13, 17, and 19.

E={2,3,5,7,11,13,17,19}E = \{2, 3, 5, 7, 11, 13, 17, 19\}E={2,3,5,7,11,13,17,19}

Calculate Probability

Count of favorable outcomes is $n(E) = 8$ . The probability is the ratio of favorable to total outcomes.

P(E)=820P(E) = \frac{8}{20}P(E)=208​

✅

B is correct because there are exactly 8 prime numbers between 1 and 20, resulting in a probability of $\frac{8}{20}$ .

Core Concepts Used

Click any tag to open in AI Tutor

💡 EXAM TIP

Understanding prime sequences is essential for both probability and number series questions in RRB exams.

Was this solution helpful?

Loading discussion...