What is probability?
Probability measures how likely something is, from 0 (it never happens) to 1 (it always happens), often written as a percent from 0% to 100%. When every outcome is equally likely, it is the number of ways the event can happen divided by the number of possible outcomes.
The chance something happens and the chance it doesn’t always add up to 100%. Over many tries, the share of times it happens gets closer and closer to its probability.
Source OpenStax · Introductory Statistics 2e, 3.1 Terminology ↗Common Core State Standards · Grade 7, probabilities of compound events (7.SP.C.8) ↗
How to calculate probability
Here it is with your numbers:
- P = 1 ÷ 6
- P = 16.6667%
It means that over many tries, it happens in 16.6667% of them, and doesn’t in 83.3333%.
Two events are independent when one happening doesn’t change the chance of the other, like two coin flips. Then the chance of both is the two chances multiplied, and the chance of at least one is the two added, minus the chance of both (so it isn’t counted twice).
Source OpenStax · Introductory Statistics 2e, 3.3 Two Basic Rules of Probability ↗
Chance of at least once, by number of tries
For the chance each try in the “At least once” calculator (10% to start). More tries make it more likely, but never quite certain.
| Tries | At least once |
|---|---|
| 1 | 10.0000% |
| 2 | 19.0000% |
| 3 | 27.1000% |
| 5 | 40.9510% |
| 10 | 65.1322% |
| 20 | 87.8423% |
| 50 | 99.4846% |
| 100 | 99.9973% |
Probability examples
| Event | Chance | Percent |
|---|---|---|
| Heads on one coin flip | 1/2 | 50% |
| A 6 on one roll of a die | 1/6 | 16.6667% |
| An ace from a deck of 52 cards | 1/13 | 7.6923% |
| Double six with two dice | 1/36 | 2.7778% |
| At least one head in 3 flips | 7/8 | 87.5% |
FAQs
What is the basic formula for probability?
When every outcome is equally likely, probability = the number of ways the event can happen ÷ the total number of possible outcomes. Rolling a 1 or a 2 on a die is 2 ÷ 6, which is 1/3, or 33.3333%.
Source OpenStax · Introductory Statistics 2e, 3.1 Terminology ↗
What is the probability of 1 out of 7?
1 out of 7 is 1/7, which is 14.2857% (1 ÷ 7 = 0.142857…, times 100). The chance it doesn’t happen is 6/7, or 85.7143%.
How do I calculate probability as a percentage?
Divide, then multiply by 100. A probability is a number from 0 to 1; 1/4 is 0.25, which is 25%. To go back, divide the percent by 100.
How to calculate pa ∩ b?
P(A ∩ B) is the chance that A and B both happen. If they are independent (one doesn’t change the chance of the other), multiply: P(A and B) = P(A) × P(B), so two coin flips both landing heads is 50% × 50%, which is 25%. If they aren’t independent, use P(B) × P(A given B).
Source OpenStax · Introductory Statistics 2e, 3.3 Two Basic Rules of Probability ↗
How to calculate probability of 3 independent events?
Multiply all three chances, using the multiplication rule twice: three heads in a row is 50% × 50% × 50%, which is 12.5%.
What is the probability of getting at least one?
Take the chance of getting none away from 100%. With a 10% chance each try, missing 10 times in a row is 90% to the power 10, which is 34.8678%, so the chance of at least one is 65.1322%.
Can the probability of an event be 2?
No. A probability is always between 0 and 1 (0% and 100%): 0 means it can never happen and 1 means it always happens.
Source OpenStax · Introductory Statistics 2e, 3.1 Terminology ↗
Sources
- OpenStax: Introductory Statistics 2e, 3.1 Terminology
- OpenStax: Introductory Statistics 2e, 3.3 Two Basic Rules of Probability
- Common Core State Standards: Grade 7, probabilities of compound events (7.SP.C.8)