Basic Math and Pre-Algebra

PART 4. The State of the World

CHAPTER 18. Probability

Relative Frequency

The frequency with which something happens is how often it happens, and that can be important information. It’s probably good to know that I found money I had forgotten about in my coat pocket four times. But there’s another piece of information that’s missing. I found money four times, but was that four times last week? Four times last month? Four times last year? Four times in my life? The answer to that makes the “four times” information more useful.

The relative frequency of an event is a number between zero and one that compares the number of times something happens to the total number of things that happened. If I found money in my pocket four times last week, that’s 4 days out of 7 days, or a relative frequency of 4/7. If it was four times last year, the relative frequency is 4/365.

DEFINITION

The relative frequency of an event is the ratio of the number of times it occurs to the total number of events observed.

Suppose you watched TV one evening and kept track of the commercials that aired in the few hours you watched. Here’s your record.

Commercials on Tuesday Night from 8 p.m. to 9 p.m.

The chart tells you that more of the commercials you viewed were for other TV shows than anything else, but is 6 a lot? Six out of eight would be a lot, but you saw more than eight ads. Six out of a hundred would not be a lot, but you didn’t sit through a hundred ads. How many did you watch? Add up the column. Then you can compare each of the counts to the total to get the relative frequency.

Commercials on Tuesday Night from 8 p.m. to 9 p.m.

Those relative frequencies are helpful in getting a sense of how the numbers relate to one another. You now know that almost one-fourth of the commercials you saw were for other TV shows, but also that one-fifth of them were for retail stores. You can also use the relative frequencies to make some predictions, or at least to talk about your expectations.

Suppose next Tuesday night you sit down to watch TV again, but you see 35 commercials instead of 25. You know that 20 percent of the ads you saw last time were for retail stores, so you can say that you’d expect about 7 of the 35 to be for stores, and 8 or 9 to be for other TV shows. You’d have a sense of what you’re likely—and not likely—to see.

Relative frequency is a way to use your observations of events to get a sense of the probability of those events, or how likely they are to occur. If 12 percent of the commercials you saw on one evening were for phones and tablets, you would expect that on the next Tuesday night at the same hour, about 12 percent of the commercials will be for phones and tablets. You’d expect that the probability of seeing an ad for phones or tablets is about 12 percent. It’s not guaranteed. The night you made your observations might have been an unusual night, or the night you’re trying to predict might be special somehow. But you have a place to start talking about how likely something is.

DEFINITION

The probability of an event is the ratio of the number of ways the event can occur to the total number of events that can possibly occur.