NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.1
Question 17

Question.  17

If \(P(A)\) denotes the probability of an event A, then

(A)

\(P(A)<0\)

(B)

\(P(A)>1\)

(C)

\(0\le P(A)\le 1\)

(D)

\(-1\le P(A)\le 1\)

Detailed Answer with Explanation:

Step 1: Probability is a number that tells us how likely an event is to happen.

Step 2: The smallest value of probability is 0. This means the event is impossible (cannot happen at all).

Step 3: The largest value of probability is 1. This means the event is certain (will definitely happen).

Step 4: For all real situations, the probability of any event lies between 0 and 1. So, it cannot be negative (less than 0), and it cannot be greater than 1.

Step 5: Therefore, the correct condition is: \(0 \leq P(A) \leq 1\).

Final Answer: Option (C).

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