Q1. A card is drawn from a well-shuffled deck of 52. Find the probability it is a king.
Favourable outcomes (kings) = 4
Total outcomes = 52
P = 4/52 = 1/13
Probability — Class 10
Probability measures how likely something is, from 0 to 1. Compute it in one click and practise the classic dice-and-card problems.
Probability of an eventP(E) = (number of favourable outcomes) / (total number of outcomes). Always between 0 and 1.
Sure & impossible eventsP(sure event) = 1; P(impossible event) = 0.
Complementary eventsP(not E) = 1 − P(E). The event and its complement together cover all outcomes.
Probability calculator Interactive
Enter the number of favourable and total outcomes to get the probability (and its complement).
P(E) = f/t—
P(not E) = 1 − f/t—
A standard deck has 52 cards; a die has 6 faces; a coin has 2. Get the total right and the rest is easy.
Numericals practice Interactive
Probability problems with steps.
Loading…
Solved examples
Formula sheet
| Quantity | Formula |
|---|---|
| Probability | P(E) = favourable / total |
| Complement | P(not E) = 1 − P(E) |
| Range | 0 ≤ P(E) ≤ 1 |
Common mistakes & exam wins
- Probability is always between 0 and 1 (never more than 1).
- Count the TOTAL outcomes carefully — that is where most mistakes happen.
- Use P(not E) = 1 − P(E) when the "at least"/"not" wording appears.
- A standard deck: 52 cards, 4 suits, 13 of each, 4 kings, 4 aces, 26 red, 26 black.
Frequently asked questions
What is the formula for probability?
P(E) = number of favourable outcomes / total number of outcomes.
What is the range of probability?
From 0 (impossible event) to 1 (sure event).
What are complementary events?
An event E and "not E"; they satisfy P(E) + P(not E) = 1.