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# Probability | Lesson

## What is a probability?

A probability indicates the chance that an
event
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".
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

## 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.
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
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:
1. 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.
2. Solve for the unknown quantity.

TRY: CALCULATING A PROBABILTY
A box contains 5 red, 10 green, and 20 orange candies. If one candy is selected randomly from the box, what is the probability that the selected candy will be red?

TRY: CALCULATING A QUANTITY FROM A PROBABILITY
A gumball machine contains red, blue, and green gumballs. There are 70 red gumballs and 50 blue gumballs. When the handle of the machine is turned, one gumball is randomly dispensed. If the probability of getting a red gumball is start fraction, 1, divided by, 3, end fraction, how many green gumballs are in the machine?

TRY: COMPARING PROBABILITIES
Doughnut VarietyNumber of Doughnuts
Cream filled16
Plain22
Jelly filled12
The table above shows the number of doughnuts in a bakery display case by variety. If a doughnut is chosen at random from the display case, which of the following statements is true?

TRY: CALCULATING A PROBABILITY USING A TABLE
ManWomanChildTotal
First class1751446325
Second class1689324285
Third class46216579706
Total8054021091, comma, 316
The table above shows data about the passengers aboard the Titanic. If a passenger who traveled on the Titanic is selected at random, what is the probability that the selected passenger was someone who traveled in first class?
percent

## 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:
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
The probability that event A will not happen is:
P, left parenthesis, start text, n, o, t, space, end text, A, right parenthesis, equals, 1, minus, P, left parenthesis, A, right parenthesis

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