Probability | Class 10 Mathematics Notes

Complementary Events and Their Probabilities

Complementary events are pairs of events where one event is the occurrence of E and the other is the non-occurrence of E, denoted as ¬E or E-bar. The sum of the probabilities of an event and its complement is always 1, i.e., P(E) + P(¬E) = 1. This is because either the event happens or it does not, covering all possible outcomes. For example, in a tennis match between Sangeeta and Reshma, if the probability of Sangeeta winning is 0.62, then the probability of Reshma winning (the complement) is 1 - 0.62 = 0.38. Similarly, for birthdays, if the probability that two friends have different birthdays is 364/365, the probability that they have the same birthday is 1/365. This concept simplifies probability calculations by allowing us to find the probability of an event by subtracting the probability of its complement from 1.

🧪 Activity: Calculate probabilities of complementary events in various scenarios such as games, birthdays, and card draws.

🔗 Connection: Understanding complementary events is essential for solving more complex probability problems and leads to applications in compound events.