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Probability Basics: Understanding Chance

Click through each step to understand the basics.

  1. What Is Probability?

    Probability is a number between 0 and 1 that represents how likely an event is to occur β€” 0 means it will never happen, and 1 means it will definitely happen.

  2. Expressing Probability as a Percentage

    The probability of a coin landing heads is 0.5, which can also be expressed as 50% β€” percentages are the more familiar way to express probability in everyday life.

  3. What Are Independent Events?

    Independent events are ones where the outcome of one doesn't affect the outcome of another β€” flipping a coin repeatedly is a classic example, since a previous result has no effect on the next flip.

  4. What Are Dependent Events?

    Dependent events are ones where the outcome of an earlier event affects the probability of the next β€” drawing a card and not replacing it before drawing another is a classic example.

  5. Sample Space and Calculating Probability

    The probability of rolling a 3 on a die is 1 out of the 6 possible outcomes, or 1/6.

  6. What Is the Gambler's Fallacy?

    Thinking that because a coin has landed heads five times in a row, it must be 'due' for tails is the gambler's fallacy β€” in reality, each flip's probability remains independently 50%.

  7. Probability in Everyday Life

    From the chance of rain in a weather forecast to lottery odds to drop rates in video games, probability shows up everywhere from weather to entertainment.

Why Understanding Probability Matters

From the chance of rain in a forecast to the odds of winning the lottery, probability is woven into daily life. Understanding the basic principles of probability helps you make more rational decisions under uncertainty.

Probability Can Also Be Updated With New Information

Probability can be recalculated as new information becomes available β€” this way of thinking is worth understanding in its own right, as a natural next step from the basics covered here.

Frequently Asked Questions

If a probability is 0, does that mean it can never happen?

That's generally how it's interpreted, but for continuous values there are theoretical exceptions where an event with probability 0 can still technically occur.

If someone won the lottery, doesn't that prove the probability was wrong?

No β€” a very low probability doesn't mean something can't happen, only that it happens rarely. Given enough attempts, even low-probability events do occur.