NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.1
Question 25

Question.  25

Someone is asked to take a number from 1 to 100. The probability that it is a prime is

(A)

\(\dfrac{1}{5}\)

(B)

\(\dfrac{6}{25}\)

(C)

\(\dfrac{1}{4}\)

(D)

\(\dfrac{13}{50}\)

Detailed Answer with Explanation:

Step 1: Probability means

\[ P(E) = \dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}} \]

Step 2: Here, the experiment is: choosing one number from 1 to 100.

Total outcomes = 100 (because there are 100 numbers from 1 to 100).

Step 3: Favourable outcomes = numbers that are prime.

Prime numbers are those which have exactly 2 factors: 1 and itself.

Step 4: Count prime numbers between 1 and 100. There are 25 prime numbers in this range.

Step 5: So, probability = \( \tfrac{25}{100} \).

Step 6: Simplify the fraction: \( \tfrac{25}{100} = \tfrac{1}{4} \).

Final Answer: Option C (\( \tfrac{1}{4} \)).

NCERT Exemplar Solutions Class 10 – Mathematics – CHAPTER 13: Statistics and Probability – Exercise 13.1 | Detailed Answers