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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A probability is a number from 0 to 1 that measures how likely an event is. When all outcomes are equally likely, count the outcomes in the event and divide by the number in the sample space. When they are not equally likely, estimate the probability from an experiment using relative frequency.
For two events, A ∩ B means both happen and A ∪ B means at least one happens. If you add P(A) and P(B), the overlap is counted twice, so you subtract it once. Events that cannot happen together are mutually exclusive and have no overlap.
A Venn diagram, a tree diagram or a table of outcomes keeps the counting organised. "At least one" is usually quickest as 1 minus the probability of none.
Students add P(A) and P(B) for any two events and forget to subtract P(A ∩ B). Add without subtracting only when the events are mutually exclusive.
Answer: P(both) = 3/40 = 0.075.
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