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Conditional Probability

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Seth Roy

on 24 September 2016

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Transcript of Conditional Probability

A Statistical Analysis of Bob Ross Paintings
Conditional Probability
The probability of a particular result happening, given a separate thing happening.

In Football: A team that leads by 7 points at halftime has about a 76% chance to win the game, according to Advanced NFL Stats.
What is Conditional Probability?
What's Bob Ross
got to do with it?
If you picked any one of Bob Ross' paintings from his 381 episodes of "The Joy of Painting," what is the probability that it would contain a tree?
What is the probability that, if Ross paints one tree, he will paint a second? Remember: 91% of his paintings contain a tree. 85% of his paintings contain two (or more) trees.
Conditional Probability
Using our data (courtesy of FiveThirtyEight), we can find out the conditional probability of finding specific elements in a painting
Clouds on the beach
44% contain clouds
9% contain a beach
7% contain clouds & a beach

What is the probability that a picture with clouds will include a beach?
Clouds and Beaches, cont.
Divide the "joint probability" by the "probability of the given." What is the probability that a beach photo contains a cloud?
Chance that a beach photo contains a cloud: .07/.09 = .78 (or 78%)
Chance that a photo w/ a cloud also contains a beach: .07/.44 = .16 (or 16%)
What percentage of paintings with mountains featured have snowy mountains? 39% of the paintings have mountains; 26% of the paintings have snow-covered mountains
Ross painted man-made structures in 22 percent of paintings. He painted cabins in 18 percent of paintings. If a painting includes a man-made structure, what is the probability that it is a cabin?
Source: FiveThirtyEight.com:
I thought this was a Sports Stats Class
Conditional Probability is used in predicting outcomes.

The Indianapolis Colts are expected to be a Playoff team this year, yet going into Sunday they were 0-2. By looking at past results, we can see how many 0-3 teams have made the playoffs. The Colts came back to beat the Chargers, and are now 1-2. What is the probability the 1-2 Colts will make the Playoffs?

5 Teams since 1990 have gone 0-3 and made the Playoffs.
According to NFL.com, an 0-3 team has a 2.8% chance to make the Playoffs, while a 1-2 team has a 23.3% chance. (2-1 = 54.9%; 3-0 = 75.9%)

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