254 Part 4: The State of the World
Commercials on Tuesday Night from 8 P.M. to 9 P.M.
Type of Commercial Number of Ads Relative Frequency
Cars and trucks 3 253 = 12%Food and dr ink (^2252) = 8%
Phones and tablets (^3253) = 12%
Drugs and medicines 3 253 = 12%
Security (^2252) = 8%
Retail stores 5 255 = 20%
Clothing and shoes (^1251) = 4%
Other TV shows 6 256 = 24%
To t a l 2 5
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 frequen-
cies 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.