prob

intersect is part to subtract
multiply probability percent

independent if prob a times prob b same as prob a and b meaning no more likely if one event has happened. can appky multiple probabilities

prob a or b is prob a plus prob. minus prob a and b

prob a given b

test prob a and b divided by even happen first which is b

thrn compare to see if it affects the second event

mutiply marginal probabilities to get joint in middle 

sum of prob a or b is sum of prob a given b plus prob b

chance boots manufactured in country a 

dont forget test for false positives by dividing by prob positive no cancer then add correct result

numerator is pos given cancer times cancer

above is posterior probability which is chance after getting tested