7th Grade Probability and Probability Models Lesson (Free PDF)

Q: How do I find the probability of an event not happening?

Subtract the probability of the event from 1. If P(rain) = 0.35, then P(no rain) = 0.65.

7th Grade math lesson: Probability and Probability Models – Maths PDF

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This probability models lesson for 7th Grade covers probability and probability models (Common Core 7.SP.C.5, 7.SP.C.6, 7.SP.C.7), with a free PDF to print.

Probability is a number from 0 to 1 that measures how likely an event is. When outcomes are equally likely, the theoretical probability is the number of favorable outcomes divided by the total number of outcomes. The relative frequency from many trials approximates the probability. The probabilities in a model always add up to 1.

Grade 7 · Common Core State Standards: 7.SP.C.5, 7.SP.C.6, 7.SP.C.7

Key facts in this probability models lesson

Key facts

Probability is between 0 (impossible) and 1 (certain).
Equally likely outcomes: \(P = favorable \div total\).
Relative frequency = number of times the outcome happens ÷ number of trials.
The probabilities of all outcomes in a model add up to 1.
\(P(not A) = 1 – P(A)\).

What is probability?

The probability of an event is a number between 0 and 1 that tells how likely the event is. A probability near 0 means unlikely, near \(\frac{1}{2}\) means about as likely as not, and near 1 means likely.

Probability is a number from 0 (impossible) to 1 (certain). Landing heads on a fair coin has probability 1/2.

An event with probability 0 is impossible, such as rolling a 7 on a standard die. An event with probability 1 is certain, such as rolling a number less than 7.

How do you find theoretical probability?

Theoretical probability

When all outcomes are equally likely: \(P(event) = number of favorable outcomes \div total number of outcomes\). This is called a uniform probability model.

This spinner has 8 equal sections: 4 red, 2 blue, 2 green. P(red) = 4/8 = 1/2.

On the spinner, 4 of the 8 sections are red, so \(P(red) = \frac{4}{8} = \frac{1}{2}\). The probability of an event that does not happen is \(1 – P(event)\), so \(P(not red) = \frac{1}{2}\).

What is relative frequency?

If you repeat an experiment many times, the relative frequency of an outcome is the number of times it happens divided by the total number of trials. It is an approximation of the probability, and it gets closer to the theoretical value as the number of trials grows.

In 60 tosses, 38 heads gives a relative frequency of 38/60, about 0.63.

Heads came up 38 times in 60 tosses, so the relative frequency is \(\frac{38}{60} ≈ 0.63\), while the theoretical probability is 0.5. With only 60 trials, some difference is expected.

What is a probability model?

A probability model lists all outcomes with their probabilities. In a uniform model each outcome has the same probability. In a non-uniform model the probabilities differ, but they always add up to 1.

The probabilities in a model add up to 1.

You can use a probability to predict. If the chance of rain is \(0.35\), you expect rain on about \(0.35 \times 20 = 7\) of the next 20 days.

Probability models lesson: questions and answers

What does a probability of 0.5 mean?

It means the event is as likely to happen as not to happen, like heads on a fair coin.

What is the difference between theoretical and experimental probability?

Theoretical probability is found by reasoning about equally likely outcomes. Experimental probability, or relative frequency, comes from repeating an experiment and counting.

Why do relative frequencies differ from theoretical probabilities?

Chance causes variation in small numbers of trials. With many more trials, the relative frequency usually gets closer to the theoretical probability.

What is a uniform probability model?

A model where every outcome has the same probability, like rolling a fair die where each face is \(\frac{1}{6}\).

How do I find the probability of an event not happening?

Subtract the probability of the event from 1. If \(P(rain) = 0.35\), then \(P(no rain) = 0.65\).

How to use this probability models lesson

Read the definitions first, then follow the worked method line by line and redo the example on paper without looking. When every step makes sense, move on to the worksheet, then check yourself with the quiz.

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