Introduction to Probability

Probability is a way to measure how likely something is to happen. We often use words like "impossible," "unlikely," "likely," or "certain" to describe the chances of different things happening. For example:

• Impossible: It can't happen, like getting a $7$ when rolling a regular $6$-sided die.

• Likely: It probably will happen, like it raining during winter. With probability, we use numbers to describe how likely something is. These numbers range from $0$ to $1$:

• $0$ (Impossible): It will never happen.

• $1$ (Certain): It will definitely happen.

• $0.5$ (Even Chance): It's just as likely to happen as not, like flipping a coin and getting heads or tails.

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The Probability Scale

We can use a probability scale to show how likely something is. Here's how it works:

Probability Number	Description	Example
$0$	Impossible	Rolling a $7$ on a $6$-sided die
$0.25$	Unlikely	Picking a red marble from a bag with mostly blue marbles
$0.5$	Even Chance	Flipping a coin and getting heads
$0.75$	Likely	Choosing a green marble from a bag with mostly green marbles
$1$	Certain	The sun will rise tomorrow

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How Do We Calculate Probability?

To find the probability of something happening, we use a simple formula:

$\text{Probability} = \frac{\text{Number of successful outcomes}}{\text{Total number of possible outcomes}}$

• Successful outcomes are the ones you are interested in.
• Total outcomes are all the possible outcomes.

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Key Points to Remember:

• Probability is always a number between $0$ and $1$. If the probability is $0$, it's impossible. If it's $1$, it's certain.
• The closer the probability is to $1$, the more likely it is to happen. The closer it is to $0$, the less likely it is to happen.
• The sum of all probabilities in a situation is $1$. For example, the probability of flipping heads or tails is $0.5 + 0.5 = 1$.

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