## Google and Conditional Probability

Conditional probability is one of my favorite topics to teach. Whereas normal probability calculations simply compare *favorable outcomes *to *total* *outcomes*, conditional probability allows us to consider the impact of certain knowledge on the likelihood of those outcomes.

For example, the probability of rolling a 6 on a six-sided die is 1/6, but if it is known that the number showing is greater than 3, then the conditional probability that a 6 is rolled is 1/3.

There are many applications of conditional probability, but a recent “Math Encounter” from the Museum of Math made me aware of an application of conditional probability that all of us see on a regular basis: Google search autocomplete.

Suppose I type in the search term “under”:

Here, Google is trying to *autocomplete *my search query. In essence, Google is trying to guess the next word I’m going to type. How does it make its guess? It computes a conditional probability!

Google has a lot of data on when words follow other words. When I enter “under” into the search bar, Google looks for the word/phrase with the highest conditional probability of being next. Here it turns out to be “armour”; the word with the second highest conditional probability is “world”, and so on.

Naturally, as more information is provided, the conditional probabilities change.

A fascinating, and perhaps surprising, application of a powerful mathematical idea!

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