Find the probability of an event.
The count of outcomes that satisfy your event is divided by the total number of possible outcomes.
Probability: Favourable outcomes ÷ Total outcomes
Probability puts a number on how likely something is. This calculator uses the classical definition: divide the number of outcomes that make your event happen by the total number of equally likely outcomes. The answer is shown both as a decimal between 0 and 1 and as a percentage.
It suits the problems in Class 9 and 10 NCERT chapters and in aptitude tests: drawing a red ball from a bag, rolling a number greater than 4 on a die, picking a king from a deck of cards or a defective bulb from a batch. It also helps in everyday reasoning, such as your chance of being picked in a lucky draw where 3 winners are chosen from 250 entries. Getting the count of favourable and total outcomes right is most of the work.
1. Describe the experiment clearly, such as rolling one fair die or drawing one card from a well-shuffled deck of 52.
2. List or count the total number of possible outcomes, making sure each is equally likely.
3. Count the favourable outcomes, the ones where your event happens.
4. Compute P(E) = favourable ÷ total.
5. Multiply by 100 to express it as a percentage.
6. Check that the answer lies between 0 and 1. A value above 1 means the favourable count was wrong.
The formula P(E) = favourable ÷ total rests on one assumption: every outcome is equally likely. A fair coin, a fair die and a well-shuffled deck satisfy it. If the outcomes are not equally likely, such as a cricket match where one team is much stronger, counting outcomes gives the wrong answer. In that case you need experimental probability, based on how often an event happened in many trials, or a model built from data.
Experimental or empirical probability is the number of times an event occurred divided by the number of trials. If you toss a coin 20 times you may get 13 heads, which is 0.65, far from 0.5. The law of large numbers says that as trials increase, the experimental value tends to settle near the theoretical value. That is why a few trials prove little, and why insurers and weather forecasters rely on large datasets.
A probability of 0 means impossible and 1 means certain. Since favourable outcomes can never exceed the total, a correct setup always gives a value in this range. The probability that the event does not happen is 1 − P(E). Odds are a different way to express the same information: odds in favour are favourable to unfavourable, so a probability of 1/4 corresponds to odds of 1 to 3, not 1 to 4.
A bag at a school fete holds 20 marbles, of which 7 are blue. Kabir draws one marble without looking and wants the chance that it is blue.
Answer: Probability 0.35; As a percentage 35%
Assuming outcomes are equally likely when they are not, such as treating win, lose and draw as one-third each.
Counting the total wrongly for two dice. There are 36 ordered outcomes, not 11 possible sums.
Double counting overlapping outcomes, such as counting the king of hearts both as a king and as a heart.
Entering a favourable count larger than the total. The calculator does not block this, so check the answer stays at or below 1.
Confusing probability with odds. A 1 in 5 chance means odds of 1 to 4.
Solving NCERT and board exam questions on dice, coins, cards and marbles.
Estimating the chance of winning a lucky draw from the number of prizes and entries.
Quality control, such as the chance of picking a defective item from a known batch.
Game design, to check how often a particular card or roll will appear.
Building intuition before moving on to conditional probability and distributions.
What does a probability of 1 mean?
A probability of 1 means the event will definitely happen. A probability of 0 means it is impossible. Everything else falls somewhere in between.