Basic Math and Pre-Algebra

PART 4. The State of the World

CHAPTER 18. Probability

Theoretical Probability

Relative frequency is useful in estimating the probability of events, but you don’t always have to do all that observing and recording. Sometimes you can make an estimate of the probability of some event based on things you already know (or can reasonably assume.) If you toss a coin, you know it has two sides—a head and a tail—and you assume that heads and tails are equally likely. As a result, you expect that the probability of heads is 1/2 or 50 percent, and the probability of tails is also 50 percent. If you have a bag containing 10 marbles, 3 red, 4 blue, 2 green, and 1 yellow, and you are planning to draw out one marble without looking, you can reasonably expect that the probability that it will be red is 3/10 or 30 percent, and the probability that it will be blue is 4/10 or 40 percent. In the same way, the chance of drawing a green marble will be 20 percent, and the chance of a yellow will be 10 percent.

The probability of something happening is a number between zero and one that tells you how likely the event is. That number can be written as a fraction, a decimal, or a percent. If the probability is zero, the event is impossible. It can’t happen. If the probability is one, it’s absolutely certain to happen. It’s a sure thing. If you draw one item out of that bag of ten marbles, the probability that it’s a kitten is 0. The probability that it’s a marble is 100 percent, or 1.

Most probabilities are somewhere in between zero and one, because most events are neither absolutely impossible nor absolutely certain. Probabilities are fractions, but you’ll often hear them expressed as percentages (a 30 percent chance of rain) or as ratios (1 in 10 chance of such-and- such happening). The probability of an event is a fraction that compares the number of ways the event can happen to the total number of things that can happen.

If you take a well-shuffled deck of cards and pick one card at random, the probability of choosing an ace is  because there are 4 aces out of 52 cards in the deck. The probability that the card will be a heart is  because 13 of the 52 cards are hearts. The probability that you will choose the ace of hearts is 1/52 because there is only one ace of hearts in the deck.