Maths: Applications and Interpretation · 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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A probability is a number from 0 to 1 that tells you how likely an event is. When all outcomes are equally likely, count the outcomes you want and divide by the total number of outcomes. A sample space diagram, a Venn diagram or a tree diagram is a way to list the outcomes so that none is missed or counted twice.
For two events, ∩ means both happen and ∪ means at least one happens. A conditional probability P(A | B) is the probability of A when you already know B has happened, so you only look inside B.
Two events are independent when one does not change the probability of the other. They are mutually exclusive when they cannot happen together.
Students mix up independent and mutually exclusive. Mutually exclusive means P(A ∩ B) = 0; independent means P(A ∩ B) = P(A) × P(B). Also, in P(A | B) divide by P(B), the event after the bar, not by P(A).
Answer: P(A | B) = 0.6, and A and B are independent because P(A | B) = P(A).
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