What is the range of probability?

Probability always lies between 0 and 1 (inclusive): 0 ≤ P(E) ≤ 1. P(E) = 0 means the event is impossible (e.g., rolling a 7 on a 6-sided dice). P(E) = 1 means the event is certain/sure (e.g., rolling a number from 1 to 6 on a 6-sided dice). The sum of the probabilities of all possible outcomes in a sample space is always 1.

What is complementary probability?

If E is an event, then 'not E' (written E' or Ē) is the complementary event — all outcomes not in E. The sum of their probabilities is always 1: P(E) + P(not E) = 1, so P(not E) = 1 − P(E). For example, if P(rain) = 0.3, then P(no rain) = 1 − 0.3 = 0.7.

What is the difference between experimental and theoretical probability?

Experimental (empirical) probability is based on actual observation: P(E) = (number of times E occurred) / (total trials). It approaches theoretical probability as trials increase. Theoretical (classical) probability is based on mathematical reasoning assuming equally likely outcomes: P(E) = (favourable outcomes) / (total equally likely outcomes). Example: Theoretically, P(Head) = 1/2. If you toss 100 times and get 48 heads, experimental P(Head) = 48/100 = 0.48.

Basic Probability

Probability • Class 9 Mathematics • NCERT • CBSE

Probability is the measure of the likelihood of an event. P(E) = (Number of favourable outcomes) / (Total number of outcomes). Probability always lies between 0 and 1. An impossible event has probability 0; a sure event has probability 1.

Key Formulas

P(E) = Favourable outcomes / Total outcomes
P(E) + P(not E) = 1
0 ≤ P(E) ≤ 1

Frequently Asked Questions

What is the range of probability?: Probability always lies between 0 and 1 (inclusive): 0 ≤ P(E) ≤ 1. P(E) = 0 means the event is impossible (e.g., rolling a 7 on a 6-sided dice). P(E) = 1 means the event is certain/sure (e.g., rolling a number from 1 to 6 on a 6-sided dice). The sum of the probabilities of all possible outcomes in a sample space is always 1.
What is complementary probability?: If E is an event, then 'not E' (written E' or Ē) is the complementary event — all outcomes not in E. The sum of their probabilities is always 1: P(E) + P(not E) = 1, so P(not E) = 1 − P(E). For example, if P(rain) = 0.3, then P(no rain) = 1 − 0.3 = 0.7.
What is the difference between experimental and theoretical probability?: Experimental (empirical) probability is based on actual observation: P(E) = (number of times E occurred) / (total trials). It approaches theoretical probability as trials increase. Theoretical (classical) probability is based on mathematical reasoning assuming equally likely outcomes: P(E) = (favourable outcomes) / (total equally likely outcomes). Example: Theoretically, P(Head) = 1/2. If you toss 100 times and get 48 heads, experimental P(Head) = 48/100 = 0.48.

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