NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.1Question 15
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.1
Question. 15
If the probability of an event is \(p\), the probability of its complementary event is
(A)
\(p-1\)
(B)
\(p\)
(C)
\(1-p\)
(D)
\(1-\dfrac{1}{p}\)
Detailed Answer with Explanation:
Step 1: The probability of an event (say event A) is given as \(p\).
Step 2: The complementary event means the event does not happen.
Step 3: In probability, the sum of an event and its complement is always 1. Mathematically: \( P(A) + P(A') = 1 \).
Step 4: Here, \(P(A) = p\). So, \( p + P(A') = 1 \).
Step 5: Rearranging, \( P(A') = 1 - p \).
Final Answer: The probability of the complementary event is \(1-p\). Hence, option (C).