Complementary events
- CBSE · NCERT Class 10, Ch 14 Probability
Two events are complementary when exactly one of them must happen, like E and not E, so their probabilities add up to 1.
Take any event E, such as drawing an ace. Its complement is not E: drawing any card that is not an ace. On each try, one of the two happens and never both. So P(E) + P(not E) = 1. This means P(not E) = 1 − P(E). Sometimes it is quicker to find P(E) and take it away from 1.
A small example
A pack of 52 cards has 4 aces. So P(ace) = 4/52 = 1/13. Then P(not an ace) = 1 − 1/13 = 12/13. You get this without counting the 48 other cards.
Where marks go
Question 38 of CBSE's 2026-27 Maths Basic sample paper is a case study on 400 printed T-shirts, of which 312 are good. Part (iii)(A) asks for the chance that a T-shirt is not good. The 2026-27 Maths Basic marking scheme uses the complement: 1 − 312/400 = 88/400 = 11/50.
The scheme prints its 2 marks as 1 + 1. Writing the 1 − P(good) line shows the examiner which method you used. See how step marking works.
Sources
Facts last checked against these sources on 30 September 2026.
About the author
Chief Architect
An engineer (B.Tech, Computer Science) with over 20 years of preparing students for entrance exams, including as Dean at FIITJEE and Vice-President at Aakash. He is the chief architect of the TRUpreBoards evaluation engine.
Mohit Sardana on LinkedIn
