Suppose we are given the following table of data. This tells us whether or not our friend will play a game of chess with us outside in the park, based on a number of weather-related conditions:
Temperature | Wind | Sunshine | Play |
Cold | Strong | Cloudy | No |
Warm | Strong | Cloudy | No |
Warm | None | Sunny | Yes |
Hot | None | Sunny | No |
Hot | Breeze | Cloudy | Yes |
Warm | Breeze | Sunny | Yes |
Cold | Breeze | Cloudy | No |
Cold | None | Sunny | Yes |
Hot | Strong | Cloudy | Yes |
Warm | None | Cloudy | Yes |
Warm | Strong | Sunny | ? |
We would like to establish, by using Bayes' theorem, whether our friend would like to play a game of chess with us in the park given that the Temperature is Warm, the Wind is Strong, and it is Sunny.
In this case, we may want to consider Temperature, Wind, and Sunshine as the independent random variables. The formula for the extended Bayes' theorem, when adapted, becomes the following:
Let's count the number of columns in the table with all known values to determine the individual probabilities.
P(Play=Yes)=6/10=3/5, since there are 10 columns with...