# Bayes’ Theorem: The Holy Grail of Data Science

1 Statistical resultsThe figure tells us that we have picked…… 148 times a blueberry from the bowl X: n(s=X, y=B)=148… 26 times a blueberry from the bowl Y: n(s=Y, y=B)=26… 51 times an orange from the bowl X: n(s=X, y=O)=51… 75 times an orange from the bowl Y: n(s=Y, y=O)=75Given these statistical numbers, we can now ask some interesting questions…What is a probability to pick a random item from bowl X?The obtain this probability that we denote as p(s=X) we must divide the number of items picked only from bowl X divided by the number N=300 of total picks..Here is n(s=X, y=B)=148 the number of blueberries picked from X and n(s=X, y=O)=51 the number of oranges picked from Y..Thus, the probability to pick any item from X looks as follows:Eq..1 Probability to pick an item from bowl X.Note: This kind of probability is called the “Prior Probability”..In Bayesian statistical inference, the prior probability is the probability of an event before new data is collected..In this case p(s=X) tells the probability for picking an item from X, without knowing which item it is exactly.Accordingly, the probability p(s=Y) to pick an item from Y is:Eq..2 Probability to pick an item from bowl Y.What is a probability to pick an orange/blueberry?This time we want to find out how likely it is to pick an orange or blueberry without considering a specific bowl..We denote these probabilities as p(y=O) and p(y=B)..The calculation is done analogously to the previous case..We are dividing the number of picks of a specific item by the number of total picks..The resulting probabilities are given by Eq..3 and Eq.. More details