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## Praxis Core Math

### Unit 1: Lesson 3

Statistics and probability- Data representations | Lesson
- Data representations | Worked example
- Center and spread | Lesson
- Center and spread | Worked example
- Random sampling | Lesson
- Random sampling | Worked example
- Scatterplots | Lesson
- Scatterplots | Worked example
- Interpreting linear models | Lesson
- Interpreting linear models | Worked example
- Correlation and Causation | Lesson
- Correlation and causation | Worked example
- Probability | Lesson
- Probability | Worked example

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# Probability | Lesson

## What is a probability?

A probability indicates the chance that an

will happen. A probability can be any number from 0 to 1.

- A probability of 0 or 0, percent means that an event will
*never*happen. - A probability of start fraction, 1, divided by, 2, end fraction or 50, percent means that an event is
*equally likely*to happen or not happen. - A probability of 1 or 100, percent means that an event will
*certainly*happen.

The probability that event A will happen is written as P, left parenthesis, A, right parenthesis.

The probability that event A will

*not*happen, P, left parenthesis, start text, n, o, t, space, end text, A, right parenthesis, is equal to 1, minus, P, left parenthesis, A, right parenthesis.### What skills are tested?

- Calculating the probability that an event will happen (or will not happen) based on a description of the situation
- Calculating the probability that an event will happen (or will not happen) based on information in a data display
- Calculating a count or quantity from a probability
- Comparing probabilities or drawing conclusions based on probabilities

## How is the probability of an event calculated?

An event could be the outcome of any random process such as the toss of a fair coin, the roll of a fair number cube, or the random selection of an item from a group.

We use the notation P, left parenthesis, A, right parenthesis to represent "the probability that event A will happen".

## How is the probability of an event calculated using information in a data display?

When calculating the probability that a randomly selected item will have certain attribute(s), the information we need may be in a data display.

In such cases,

- The
*ways A can happen*is the number of items of type A. - The number of
*possible outcomes*is the total number in the group.

## How can we calculate a count or quantity from a probability?

Sometimes we are given the probability and are asked to calculate either the number of possible outcomes or the number of ways A can happen

To solve these questions:

- Substitute known values into the equation P, left parenthesis, A, right parenthesis, equals, start fraction, start text, w, a, y, s, space, end text, A, start text, space, c, a, n, space, h, a, p, p, e, n, end text, divided by, start text, p, o, s, s, i, b, l, e, space, o, u, t, c, o, m, e, s, end text, end fraction.
- Solve for the unknown quantity.

## Your turn!

## Things to remember

A probability indicates the chance that an event will happen.

A probability can be any number between 0 and 1.

The probability that event A will happen is:

The probability that event A will not happen is:

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