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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 $0\mathrm{%}$ means that an event will never happen.
• A probability of $\frac{1}{2}$ or $50\mathrm{%}$ means that an event is equally likely to happen or not happen.
• A probability of $1$ or $100\mathrm{%}$ means that an event will certainly happen.
The probability that event $A$ will happen is written as $P\left(A\right)$.
The probability that event $A$ will not happen, , is equal to $1-P\left(A\right)$.

### 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 $P\left(A\right)$ 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:
1. Substitute known values into the equation .
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 $\frac{1}{3}$, how many green gumballs are in the machine?

TRY: COMPARING PROBABILITIES
Doughnut VarietyNumber of Doughnuts
Cream filled$16$
Plain$22$
Jelly filled$12$
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 class$175$$144$$6$$325$
Second class$168$$93$$24$$285$
Third class$462$$165$$79$$706$
Total$805$$402$$109$$1,316$
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?
$\mathrm{%}$

## 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:

## Want to join the conversation?

• how do you figure out the probability of coins
(1 vote)
• You take one side of the coin and see how many total sides there are. one side=1 both sides=2 so, 1/2. Or 50% odds of it landing on one of the sides.