CBSE Class 10 Maths Chapter 15 Notes Probability

Probability Class 10 Notes Understanding the Lesson

Theoretical probability: The theoretical (or classical) probability of an event E [denoted by P(E)] is given by
\(\mathrm{P}(\mathrm{E})=\frac{\text { Number of outcomes favourable to } \mathrm{E}}{\text { Number of all possible outcomes of the experiment }} \text { i.e., } \frac{n(\mathrm{A})}{n(\mathrm{S})}\)

Number of all possible outcomes of the experiment when the outcomes of the experiment are equally likely.

Equally likely outcomes: All the outcomes of an experiment are said to be equally likely when the chances of there occurrence are equal.
e.g. When a coin is tossed, the two possible outcomes are head and tail, which are equally likely.

Elementary event: An outcome of a random experiment is called an elementary event. e.g. In tossing a coin, possible outcomes are head and tail.
⇒ H and T are elementary events.

• The sum of the probabilities of all the elementary events of an experiment is 1.
• For an events E, P(E) + P(\(\overrightarrow{\mathrm{E}}\)) = 1, where \(\overrightarrow{\mathrm{E}}\) is the event ‘Not E’. E and \(\overrightarrow{\mathrm{E}}\) are called complementary events.
• If P(E) = 1, then E is called ‘sure or certain event’.
• If P(E) = 0, then E is impossible event.
• For any event E,
  0 < P(E) <1