Probability | Class 10 Mathematics Notes

Impossible and Sure Events

This section explains the concepts of impossible and sure (certain) events in probability. An impossible event is one that cannot happen under any circumstances. For example, getting the number 8 on a single throw of a standard six-faced die is impossible because the die only has faces numbered 1 to 6. The probability of an impossible event is 0. On the other hand, a sure event is one that is certain to happen. For example, getting a number less than 7 on a die throw is a sure event because all faces are numbered less than 7. The probability of a sure event is 1. The probability of any event E always lies between 0 and 1 inclusive, i.e., 0 ≤ P(E) ≤ 1. This range is because the number of favorable outcomes cannot be negative or greater than the total number of outcomes. These concepts help in understanding the boundaries of probability values and are fundamental in probability theory.

🧪 Activity: Identify impossible and sure events in various experiments and justify their probabilities.

🔗 Connection: Understanding impossible and sure events sets the stage for exploring complementary events and more complex probability calculations.