What it does
Probability at school starts from one idea: when every outcome is equally likely, the probability of an event is
P(E) = number of outcomes in the event / total number of outcomes.
The hard part is listing the outcomes without missing any or counting one twice. This page lists them for you. Pick two dice, one to three coins or a full deck of 52 cards, choose an event, and every outcome appears in a grid with the ones in the event shaded. The probability is shown as a fraction, in its simplest form and as a decimal, together with the chance that the event does not happen.
The second card does the experiment at random, 100, 1 000 or 10 000 times, and draws how the share of hits (the relative frequency) changes as the trials pile up. That is the experimental probability of the Class 9 chapter; the shaded count is the theoretical (classical) probability of Class 10, and Class 11 puts the two side by side. The page lets you see them meet.
To count outcomes when listing them is too long, try combinatorics calculator. When the outcomes are numbers, probability distribution explorer shows the whole spread of chances, and grouped data summarises real data you collect.
How to use it
- Choose Two dice, Coins or A deck of cards.
- Pick an event from the list. Some events take a number, such as “the sum is k” or “exactly k heads”; type it in the Number box.
- For coins, choose how many (1, 2 or 3).
- Read P(E) under the grid. Shaded cells are the favourable outcomes.
- Press 100 times, 1 000 times or 10 000 times. The blue line is the running relative frequency; the dashed line is the probability.
A worked example
Two dice are thrown. What is the probability that the sum is 7?
- There are 6 × 6 = 36 equally likely outcomes, from (1, 1) to (6, 6).
- The sum is 7 for (1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1): 6 outcomes, one diagonal of the grid.
- P(sum 7) = 6/36 = 1/6 ≈ 0.1667, and P(sum not 7) = 30/36 = 5/6.
Run it 10 000 times and the relative frequency usually lands within about 0.01 of 0.1667. With only 100 throws it can easily be 0.12 or 0.22.
Tips
- (2, 5) and (5, 2) are different outcomes. Think of one red die and one blue die.
- P(E) is always between 0 (impossible) and 1 (certain), and P(E) + P(not E) = 1.
- More trials do not force the frequency to equal the probability; they only make big gaps rarer.
Check yourself
Four fresh questions each time: a dice sum, a number of heads, a card event and a “does not happen” question. Fractions such as 1/6 are accepted. Nothing is saved.
FAQ
Why is a sum of 7 the most likely? It has the most ways to happen: six, one for each value of the first die.
Is this from the NCERT book? It covers the same topics with fibub’s own examples. fibub is not part of NCERT.
Where the numbers come from
- Classical probability (favourable outcomes over equally likely outcomes) and relative frequency are standard school mathematics. Written for fibub; the simulation uses the public-domain mulberry32 generator.
- Checked against counts done separately in Python with itertools.product: two dice (sum 7 = 6/36, sum at least 10 = 6/36, prime sum = 15/36, even product = 27/36), three coins (exactly one head = 3/8) and the 52-card deck (26 red, 12 face, 6 red face cards).
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.