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

Question.  13

Which of the following cannot be the probability of an event?

(A)

\(\dfrac{1}{3}\)

(B)

0.1

(C)

3%

(D)

\(\dfrac{17}{16}\)

Detailed Answer with Explanation:

Step 1: Recall the rule of probability. The probability of any event always lies between 0 and 1 (both included). In symbols: \(0 \leq P(E) \leq 1\).

Step 2: Check each option one by one:

  • (A) \(\tfrac{1}{3}\): This is equal to 0.333… which lies between 0 and 1. ✔ Valid probability.
  • (B) 0.1: This is 0.1, which lies between 0 and 1. ✔ Valid probability.
  • (C) 3%: Percentage means “out of 100.” So, 3% = \(\tfrac{3}{100} = 0.03\). This also lies between 0 and 1. ✔ Valid probability.
  • (D) \(\tfrac{17}{16}\): Divide 17 by 16 = 1.0625. This is greater than 1. ✘ Not possible for probability.

Step 3: Since probability cannot be more than 1, option (D) \(\tfrac{17}{16}\) is not possible.

Final Answer: Option (D)

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