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The Basics of Probability Study Guide

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Updated on Oct 5, 2011

Introduction to The Basics of Probability

The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.

—CHARLES CALEB COLTON, English writer (1780–1832)

This lesson explores probability, presenting real-life examples and the mathematics behind them.

You've probably heard statements like, "The chances that I'll win that car are one in a million," spoken by people who doubt their luck. The phrase "one in a million" is a way of stating the probability, the likelihood, that an event will occur. Although most of us have used exaggerated estimates like this before, this chapter will teach you how to calculate probability accurately. Finding answers to questions like "What is the probability that I will draw an ace in a game of poker?" or "How likely is it that my name will be drawn as the winner of that vacation for two?" will help you decide if the probability is favorable enough for you to take a chance.

Finding Probability

Probability is expressed as a ratio:

Example: When you toss a coin, there are two possible outcomes: heads or tails. The probability of tossing heads is therefore 1 out of the 2 possible outcomes:

Similarly, the probability of tossing tails is also 1 out of the 2 possible outcomes. This probability can be expressed as a fraction, , or as a decimal, 0.5. Since tossing heads and tails have the same probability, the two events are equally likely.

The probability that an event will occur is always a value between 0 and 1:

  • If an event is a sure thing, then its probability is 1.
  • If an event cannot occur under any circumstances, then its probability is 0.

For example, the probability of picking a black marble from a bag containing only black marbles is 1, while the probability of picking a white marble from that same bag is 0.

An event that is rather unlikely to occur has a probability close to zero; the less likely it is to occur, the closer its probability is to zero. Conversely, an event that's quite likely to occur has a probability close to 1; the more likely an event is to occur, the closer its probability is to 1.

Example: Suppose you put 2 red buttons and 3 blue buttons into a box and then pick one button without looking. Calculate the probability of picking a red button and the probability of picking a blue button.

The probability of picking a red button is or 0.4. There are 2 favorable outcomes (picking one of the 2 red buttons) and 5 possible outcomes (picking any of the 5 buttons). Similarly, the probability of picking a blue button is , or 0.6. There are 3 favorable outcomes (picking one of the 3 blue buttons) and 5 possible outcomes. Picking a blue button is more likely than picking a red button because there are more blue buttons than red ones: of the buttons are blue, while only of them are red.

Tip

Sometimes you might see probability written as a percentage: There is a 60% chance of thunderstorms tomorrow. What this means is or .

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