Independent events and total probability
Test whether two events are independent with a table, see why events that cannot happen together are not independent, and add the paths of a tree to find the probability of an outcome that can arise in several ways.
- UK: Year 12
- France: grade 11
- Germany: grade 11
- Iran: grade 11
- Afghanistan: grade 12
- Syria: grade 11
- Palestine: grade 9
- Russia: grade 10
Guide
This studio follows Afghan grade 12 chapter 8 (the product rule and independence of events, with the total probability formula under the tree) and the UK A-level probability topic.
Events A and B are independent when P(A ∩ B) = P(A) × P(B), which means knowing B does not change the chance of A. The total probability of an outcome is the sum of the probabilities of all the paths of the tree that lead to it.
Common mistakes worked on here: thinking that overlapping events are dependent, thinking that events that cannot happen together are independent, using only one path, adding the rates without weights, and taking a plain average.