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Notes
Practice Problems
For problems 1-9, use the Venn diagram below.
\(\textbf{1)}\) P (fruit)
\(\textbf{2)}\) P (not fruit)
\(\textbf{3)}\) P (fruit and vegetable)
\(\textbf{4)}\) P (fruit or vegetable)
\(\textbf{5)}\) P (fruit | vegetable)
\(\textbf{6)}\) P (vegetable | fruit)
\(\textbf{7)}\) P (fruit and not vegetable)
\(\textbf{8)}\) Are “fruit” and “vegetable” independent?
\(\textbf{9)}\) Are “fruit” and “vegetable” mutually exclusive?
\(\textbf{10)}\) Are “red” and “truck” mutually exclusive?
See Related Pages\(\)
\(\bullet\text{ Statistics Homepage}\)
\(\,\,\,\,\,\,\,\,\text{All the Best Topics…}\)
\(\bullet\text{ Conditional Probabilites}\)
\(\,\,\,\,\,\,\,\,P(A|B)=\displaystyle\frac{P(A \cap B}{P(B)}…\)
\(\bullet\text{ Independent Events}\)
\(\,\,\,\,\,\,\,\,P(A \cap B)=P(A)P(B)…\)
\(\bullet\text{ Venn Diagrams}\)
\(\,\,\,\,\,\,\,\,\)…
\(\bullet\text{ Tree Diagrams}\)
\(\,\,\,\,\,\,\,\,\)
…
\(\bullet\text{ Two-Way Tables}\)
\(\,\,\,\,\,\,\,\,\)
…
In Summary
Mutually exclusive events (aka disjoint events) are events that cannot occur at the same time. A lot of interesting probabilities come from recognizing if 2 events are mutually exclusive.
\(P\left(A \text{ or } B\right) = P\left(A\right) + P\left(B\right)\)
\(P\left(A \text{ and } B\right) = 0 \)
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