Probability
Grade 7 · Math · Study Guide
Explore how likely events are to occur using fractions, decimals, and percents to express probability.
Probability is the study of how likely an event is to happen. It is always expressed as a number between 0 and 1. A probability of 0 means something is impossible (like rolling a 7 on a standard die), and a probability of 1 means something is certain (like the sun rising tomorrow). A probability of 0.5 means equally likely to happen or not happen — like flipping a fair coin.
Theoretical probability is what you calculate by reasoning about equally likely outcomes. The formula is: P(event) = (number of favorable outcomes) ÷ (total number of possible outcomes). For a standard six-sided die, P(rolling a 4) = 1/6. The set of all possible outcomes is called the sample space.
Experimental probability is what you calculate from actual data. If you flip a coin 100 times and get heads 48 times, the experimental probability of heads is 48/100 = 0.48. Experimental and theoretical probabilities often differ, but as you do more trials, experimental probability gets closer to theoretical probability — this is called the Law of Large Numbers.
Complement of an event: the probability that something does NOT happen is 1 minus the probability that it does. If P(rain) = 0.3, then P(no rain) = 1 − 0.3 = 0.7. All probabilities for all possible outcomes in a sample space must add up to exactly 1.
Probability can be expressed as a fraction, decimal, or percent — they are all equivalent. P = 1/4 = 0.25 = 25%. Choosing the right form often depends on context: weather forecasters use percents, statisticians often use decimals, and textbook problems often use fractions.
| Probability Value | What It Means | Example |
|---|---|---|
| 0 | Impossible | Rolling a 9 on a 6-sided die |
| 0.25 (1/4) | Unlikely | Drawing a spade from a deck of cards |
| 0.5 (1/2) | Equally likely or unlikely | Flipping heads on a fair coin |
| 0.75 (3/4) | Likely | Drawing a red card from a standard deck |
| 1 | Certain | Drawing any card from a deck of cards |
| Type | How Calculated | Example |
|---|---|---|
| Theoretical | Favorable outcomes ÷ Total outcomes | P(heads) = 1/2 |
| Experimental | Observed successes ÷ Total trials | Got heads 55 times in 100 flips → 55/100 |
Key terms
- Probability
- A number between 0 and 1 that measures how likely an event is to occur
- Theoretical probability
- Probability calculated from reasoning about equally likely outcomes: P(event) = favorable ÷ total
- Experimental probability
- Probability calculated from actual data collected through experiments or observation
- Sample space
- The complete set of all possible outcomes for a probability experiment
- Complement
- The probability that an event does NOT occur: P(not A) = 1 − P(A)
Practice questions
A bag contains 3 red, 5 blue, and 2 green marbles. What is the probability of randomly drawing a blue marble?
- 3/10
- 5/10
- 2/10
- 5/7
Show answer
Answer: 5/10
A probability of 0 means an event is impossible.
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Answer: True
If P(event) = 0.35, then the probability of the complement (the event NOT occurring) is ___.
Show answer
Answer: 0.65
A coin is flipped 200 times and lands on heads 110 times. What is the experimental probability of heads?
- 1/2
- 11/20
- 9/20
- 110
Show answer
Answer: 11/20
The sum of all probabilities in a sample space always equals 1.
Show answer
Answer: True
Fun facts
- Weather forecasters calculate probability of rain using complex models with thousands of variables — but the result is the same type of 0-to-1 probability you are learning right now.
- A famous gambler named Blaise Pascal and mathematician Pierre de Fermat invented modern probability theory in the 1600s by trading letters about a gambling dispute.
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