Maths: Analysis and Approaches · Statistics and probability. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
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Conditional probability is the probability of an event when you already know that another event has happened. P(A | B) means the probability of A given B. Knowing B makes the sample space smaller: you now look only at the outcomes inside B, and ask what fraction of them are also in A.
In a table or Venn diagram, divide the number in both A and B by the total for B. In a tree diagram, the second set of branches already shows conditional probabilities, so multiply along the branches and add the routes you need.
Two events are independent when one happening does not change the probability of the other, so P(A | B) = P(A).
Dividing by the wrong probability. In P(A | B) the event after the line is the one you know has happened, so its probability goes underneath: P(A | B) and P(B | A) are usually different.
Answer: 3/7, which is about 0.429
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